Eurocodice 1 (EC1). Basi di calcolo ed azioni sulle strutture. Parte 4: Azioni su silos e serbatoi. Lingua: italiano.
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PROJECTILE MOTION CONCEPTS AND MOTION IN 2D CONCEPTSFull description
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Projectile MotionFull description
basic projectile motion problems or motion in 2D and answers for free
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Jellema 4B Omhulling - Gevels
EXERCISE # 1 Q.6
A larg largee numb number er of bull bullet etss are are fire fired d in all all directions with the same speed from ground,hat is the ma"imum area on the ground on
Q.1
A bullet is fired in a horizontal direction from
which these bullets will spread (height of gun
a towe towerr whil whilee a ston stonee is simu simult ltan aneo eous usly ly
from ground assume negligible)&
dropped from the same point then – (A)
(A) The bullet and the stone will reach the ground simultaneously simultaneously
π * g
(B) The stone will reach earlier
π**
(C) The bullet will reach earlier
g*
(B)
π + g*
(C (C)
π* +
(D)
g*
(D) Nothing can be predicted Q.7
A cannon ball has a range . on a horizontal plane- f h and h5 are the greatest heights in the two paths for which this is possible$ then–
Q.2
f T be the total time of flight of a current of (A) . ' +
water and ! be the ma"imum height attained by it from the poin pointt of pro#ec pro#ectio tion$ n$ then then !%T will be & (u ' pro#ection elocity$ elocity$
Q.3
(C) . ' + h h5
θ ' pro#ection
angle) (A) (%*) u sin θ
(B) (%+) u sin θ
(C) u sin θ
(D) *u sin θ
(B) . '
hh 5
Q.8
+h
(D) . '
h5 hh 5
Two Two stones are pro#ected with the same speed but ma6ing different angles with the horizontal- Their ranges are e7ual- f the angle
f a base baseba ball ll play player er can can thro throw w a ball ball at ma"im ma"imum um dista distance nce ' d oer oer a ground ground$$ the the
of pro#ection of one is
ma"im ma"imum um ertic ertical al height height to which which he can
other will be –
throw it$ will be (Ball hae same initial speed
(A) /y
π%/ and its ma"imum
height is y then the ma"imum height of the (B) *y
(C) y%*
(D) y%/
in each case) & (A) d%* Q.4
(B) d
(C) *d
(D) d%+
Q.9
An ob#ect ob#ect is thro thrown wn at an angle angle
α to the
α 8 901) with a elocity -
,hat is the aerage elocity of a pro#ectile
horizo horizonta ntall (01 8
between the instants is crosses half the
Then during ascent (ignoring (ignoring air drag) the
ma"imum heightheight- t is pro#ected with with a speed
acceleration –
u at an angle θ with the horizontal&
(A) ,ith which the ob#ect moes is g at all
(A) u sinθ
(B) u cosθ
(C) u tanθ
(D) u
→
points (B) Tangential to the path decreases (C) Normal to the path increases$ becoming
Q.5
e7ual to g at the highest point
An artillery piece which consistently shoots
(D) All of the aboe
its shell with the same muzzle speed has a ma"imum range of .- To hit a target which is .%* from the gun and on the same leel$ at what what ele eleat atio ion n angl anglee shou should ld the the gun gun be pointed(height pointed(height
of
gun
from
ground
Q.10
in
m%s$ at an angle of 301 with the horizontalAfter how much time the elocity ector will ma6e an angle of +21 with the horizontal (in
neglected)& (A) /01
A pro#ectile is thrown with a elocity of *0
(B) +21
(C) 301
(D) 421
Tower$ .oad No-$ :A$ ;ota (.a#-)$ :h< 04++&/0+0000 CAREER POINT, C: Tower$
upward direction) is (ta6e g ' 0m%s *)& :.=>?CT@? =T=N
98
(A) (C) (
Q.11
Q.12
/ sec
(B) %
/ – ) sec
/ sec
(D) None of these
An aeroplane was flying horizontally with a elocity of 4*0 6m%h at an altitude of +90 m,hen it is #ust ertically aboe the target a bomb is dropped from it- !ow far horizontally it missed the target (A) 000 m (B) *000 m (C) 00 m (D) *00 m rom the top of a tower of height h a body of mass m is pro#ected in the horizontal direction with a elocity $ it falls on the ground at a distance " from the tower- f a body of mass *m is pro#ected from the top of another tower of height *h in the horizontal direction so that it falls on the ground at a distance *" from the tower$ the horizontal elocity of the second body is & D D (A) * (B) * (C) (D) * *
(A) a (C)
Q.15
(B) a
*! % g
! % *g
(D) None of these
g % *!
To an obserer moing along ?ast$ the wind appears to blow from North- f he doubles his speed $ the air would appear to come from &
Q.16
(A) North
(B) ?ast
(C) North&?ast
(D) North&,est
A car A is going north&east at E06m%hr- and another car B is going south&east at 306m%hrThen the direction of the elocity of A relatie to B ma6es with the north an angle
Q.13
A bomber is moing with a elocity (m%s) aboe ! meter from the ground- The bomber releases a bomb to hit a target T as shown in
such that tanα is – (A) %4
(B) /%+
figure Then the relation between θ$ ! and is&
(C) +%/
(D) /%2
Q.17
α
A boat man could row his boat with a speed 0m%sec- !e wants to ta6e his boat from : to a point F #ust opposite on the other ban6 of the rier flowing at a speed +m%sec- !e
(A) θ '
tan –
* !g
should row his boat –
(B) θ '
tan –
* % g!
(A) at right angle to the stream
(C) θ '
tan –
! % *g
(B) at an angle of sin – (*%2) with :F up the
(D) None of the aboe Q.14
A stunt performer is to run and die off a tall platform and land in a net in the bac6 of a truc6 below- =riginally the truc6 is directly under the platform$ it starts forward with a constant acceleration a at the same instant the performer leaes the platform- f the platform is ! aboe the net in the truc6$ then the horizontal elocity u that the performer must hae as he leaes the platform is –
stream (C) at an angle of sin – (*%2) with :F down the stream (D) at an angle cos – (*%2) with :F down the stream Q.18
CAREER POINT, C: Tower$ .oad No-$ :A$ ;ota (.a#-)$ :h< 04++&/0+0000
A bus moes oer a straight leel road with an acceleration a - A boy in the bus drops a ball outside- The acceleration of the ball with :.=>?CT@? =T=N
99
respect
to
the bus
and
the
earth
are
the gun with elocities of /20 m%s and /00 m%s respectiely- ind when will they meet
respectiely & (A) a and g (B) a G g and g – a
Q.19
(C)
a*
+
g*
and g
(D)
a*
+
g*
and a (A) /%32 sec (C) /%92 sec
A man standing on a road has to hold his umbrella at /01 with the ertical to 6eep the
(B) 2%32 sec (D) / %2 sec
rain away- !e thrown the umbrella and starts running at 0 6m%h- !e finds that rain drop are hitting his head ertically- ind the speed of rain w-r-t- road&
Q.22
(A) 0 6m%s
(B) *0 6m%h
is n times the ma"imum height !$ then the
(C) 0 √/ 6m%s
(D) *0 √/ 6m%h
angle of pro#ection θ is e7ual to tan –(+%n)Q.23
Q.20
f in the case of a pro#ectile motion$ range .
n angular pro#ection motion$ the ratio of 6inetic to potential energy at the highest point
A ball A is pro#ected from origin with an
of the path is tan *θ-
initial elocity 0 ' 400 cm%s$ in a direction /41 aboe the horizontal as shown in figAnother ball B /00 cm from origin on a line /41 aboe the horizontal is released from rest at the instant A starts- then
how
Q.24
far
An aeroplane flies horizontally at height h with a constant speed - An anti&aircraft gun
will B hae fallen when it is hit by A –
fires a shell at the plane when it is ertically aboe the gun-
The minimum muzzle
elocity of the shell re7uired to hit the plane is -------------- at an angle --------------- with the horizontalQ.25
Q.21
(A) 90 cm
(B) E0 cm
(D) 40 cm
(D) 30 cm
A particle is pro#ected with a elocity u so that its range on a horizontal plane is twice the greatest height attained-
The range of
pro#ection is -------------------------
Two guns are pointed at each other one upwards at an angle of eleation of /01 and other at the same angle of depression$ the muzzle being /0 m apart- f the charges leae
CAREER POINT, C: Tower$ .oad No-$ :A$ ;ota (.a#-)$ :h< 04++&/0+0000
:.=>?CT@? =T=N
100
EXERCISE # 2 (A) sec Q.5
(B) * sec
(C) / sec (D) + sec
A shell is fired from a gun from the bottom of a hill along its slope- The slope of the hill is
Q.1
A ball is pro#ected upwards from the top of
α ' /01$ and the angle of the barrel to the
tower with a elocity 20 m%s ma6ing an angle
horizontal
the instant of throwing will the ball reach the
from the gun at which shell will fall –
ground –
(A) 0 m
(B) *0 m
(C) /0 m
(D) +0 m
(A) * s Q.2
(B) 2 s
(C) 4 s
the shell is * m%sec- Then distance of point
(D) 9 s
A particle moes in the plane "y with elocity H ' 6 iH G 6 * " H# $ where H i and # are
Q.6
of /90m aboe sea leel it launches a
and 6 * are constants- At the initial moment of
missile towards the target- The initial elocity
time the particle was located at the point " ' y ' 0 then the e7uation of the particle5s
of the missile is +0 m%s in a direction
(A) y '
(C) y '
*6 * *6 6 *
"*
"*
(B) y '
(D) y '
6 * *6
*6 * 6
where tanθ ' 9%+0- Then the time of flight of "*
the missile from the instant it was launched until it reaches sea leel is nearly –
"*
(A) 0 sec
(B) 2 sec
(C) *0 sec
(D) *2 sec
A boy throws a ball with a elocity 0 at an angle α to the horizontal- At the same instant
Q.4
θ below the horizontal
ma6ing an angle
tra#ectory y (") is –
6
An aircraft dries towards a stationary target which is at sea leel and when it is at a height
the unit ectors of the " and y a"es$ and 6
Q.3
β ' 301- The initial elocity of
/00 with the horizontal- The height of the tower is 40m- After how many seconds from
Q.7
A boat moes relatie to water with a elocity
he starts running with uniform elocity
which is %n times the rier flow elocity- At
(minimum) to catch the ball before it hits the
what angle to the stream direction must be
ground- To achiee this$ he should run with a
boat moe to minimize drifting
elocity of&
(A) π%*
(A) 0 cosα
(B) 0 sinα
(C) 0 tanα
(D)
D0* tan α
(C)
π
*
(B) sin – (%n) G sin –(%n)
(D)
π
*
– sin –(%n)
A golfer standing on leel ground hits a ball with a elocity of u ' 2* m%s at an angle
α
Q.8
A particle is pro#ected with a speed from a
aboe the horizontal- f tan α ' 2%*$ then the
point = ma6ing an angle of /01 with the
time for which the ball is at least 2m aboe
ertical- At the same instant$ a second particle
the ground (i-e- between A and B) will be
is thrown ertically upwards from a point A-
(ta6e g ' 0 m%s*) –
The two particle reach !$ the highest point on the
parabolic
path
simultaneously- Then ratio
of D
particle is&
one
Q.12
A particle is pro#ected from a point = with a elocity u in a direction ma6ing an angle
α
upward with the horizontal- After some time at point : it is moing at right angle to its initial direction of pro#ection- The time of
(A) / (C)
*
* /
(B) * (D)
flight from = to : is& u sin α (A) g
/
/ *
(C)
u tan α g
(B) (D)
u cos ecα g
u sec α g
A pro#ectile can hae the same range . for
Q.9
two angles of pro#ection when pro#ected with
Q.13
the same speed- f t and t* be the times of
ma"imum horizontal range with the same
flight in two cases$ then the product of times
elocity of pro#ection is&
of flight will be& (A) tt* ∝ .
(B) tt* ∝ . *
(C) tt* ∝ %.
(D) tt* ∝ %. *
f . is the range of a pro#ectile on a horizontal plane and h its ma"imum height$ then
*
(A) *h (C) *. G
Q.10
The height y and the distance " along the horizontal plane of a pro#ectile on a certain planet (with no surrounding atmosphere) are
Q.14
(B)
.
Eh *
h*
(D) *h G
E.
.
Eh
A particle is thrown oer a triangle from one end of a horizontal base and grazing the
gien by y ' (Et – 2t*) meter and " ' 3t meter
erte" falls on the other end of the base- f
where t is time in seconds- The elocity with
α
and β be the base angles and θ the angle of
which the pro#ectile is pro#ected is –
pro#ection then correct relation between ( θ)$
(A) E m%s
(α) and (β)is&
(B) 3 m%s (C) 0 %s
(A) tan α ' tanθ G tanβ
(D) Can not be determined
(B) tan θ ' tanα G tan β (C) tan θ ' tanα – tan β
Q.11
Three pro#ectile A$ B and C are thrown from
(D) tan β ' tanθ G tan α
the same point in the same plane- Their tra#ectories are shown in the figure- Then which of the following statement is true –
Q.15
A particle is released from a certain height ! ' +00 m-
Due to the wind the particle
gathers the horizontal elocity " ' ay where a ' √2 sec – and y is the ertical displacement of the particle from point of release$ then the horizontal drift (displacement) of the particle when it stri6es the ground is–
(A) The time of flight is the same for all the
three
(A) *-34 6m
(B) E-34 m
(C) -34 6m
(D) 2- 6m
(B) The launch speed is greatest for particle C (C) The horizontal elocity component is greatest for particle C (D) All of the aboe
Q.16
n the aboe 7uestion find the speed with which the particle stri6es the ground – (A) 2 6m%s
(B) 0-9 6m%s
(C) 9 6m%s
(D) –-009 6m%s
(C) The minimum time in which he can cross d
rier is Q.17
Two particles A and B start simultaneously from the same point and moe in a horizontal
(D) !e can not reach A if u I Q.20
plane- A has an initial elocity u due east
A train carriage moe along the "&a"is with a →
uniform acceleration a - An obserer A in
and acceleration a due north- B has an initial
the train sets a ball in motion on the
elocity u * due north and acceleration a * due
frictionless floor of the carriage with the
east- Then –
→
(A) They must collide at some point
elocity
u relatie to the
carriage- The
(B) They will collide only if a u ' a*u*
direction u of ma6es an angle θ with the "&
(C) Their paths must intersect at some point
a"is- @et B be an obserer standing on the
(D) f u I u* J a 8 a*$ the particles will
ground outside train- The path of ball will be&
→
(A) A straight line with respect to obserer A
hae the same speed at some point
(B) A straight line with respect to obserer B Q.18
A large rectangular bo" falls ertically with
(C) A parabola with respect to obserer A
acceleration a- A toy gun fi"ed at A and aimed
(D) A parabola with respect to obserer B
at C fires a particle :- Then – Q.21
Two particles are pro#ected from the same point with the same speed$ at different angles
θ and θ* to the horizontal- Their times of flight are t and t* and they hae the same horizontal range- Then– (A) : will hit C if a ' g
t
(A)
(B) : will hit the roof DC if a I g
t*
(C) : will hit wall BC if a 8 g (D) either of A$ B J C depending on speed of :Q.19
(C)
A man who can swim at a speed relatie to
' tan θ
t sin θ
(B)
t*
'
sin θ *
t t*
' tan θ*
(D)
θ G θ*
' 901
the water wants to cross a rier of width d flowing with a speed u- The point opposite him across the rier is A(A) !e can reach the point A in time d% (B) !e can reach the point A is time d *
−
u*
Q.22
An aero plane flies along straight line from A to B with speed and bac6 again with the same speed- There is a steady wind speed wThe distance between A and B is d- Total time for the round trip – (A) is
*d *
−w
line AB-
*
if the wind blows along the
(B) is
*d * − w *
if
the
wind
blows
perpendicular to the line AB-
*+ If oh &sse$ion "n% 'e"son "$e $ue u 'e"son is no !o$$e! e#l"n"ion of he &sse$ion. *C+ If &sse$ion is $ue u he 'e"son is f"lse.
(C) is always increased by the presence of
*/+ If &sse$ion is f"lse u 'e"son is $ue.
windQ.24
(D) depend on the direction of wind-
&sse$ion Two balls of different masses are
thrown ertically up with same speed- They will pass through their point of pro#ection in the downward direction with the same speedQ.23
'e"son
Tra#ectory of particle in a pro#ectile motion is gien as y ' " –
"* E0
The
ma"imum
height
and
downward elocity attained at the point of pro#ection are independent of the mass of the
- !ere$ " and y are in
ball-
metres- or this pro#ectile motion match the Q.25
following with g ' 0 m%s *Column-I
&sse$ion A pro#ectile is thrown with an H ) m%s- f range of initial elocity of (aHi + b #
Column -II
pro#ectile is ma"imum than a ' b(A)Angle of pro#ection (B) Angle of elocity
(:) *0 m
'e"son n pro#ectile motion$ angle of
(F) E0 m
pro#ection is e7ual of +2L for ma"imum range
with horizontal after +s
condition-
(C) a"imum height
(.) +21
(D) !orizontal range
(K) tan –
Q.26
*
&sse$ion Keparation between two particle
is ma"imum when component of relatie elocity of particles along line #oining them is zero'e"son At ma"imum separation elocity of
The following quesions !onsiss of wo s"emens e"!h, #$ine% "s &sse$ion "n% 'e"son. (hile "nswe$ing hese quesions )ou "$e o !hoose "n) one of he following fou$ $es#onses. *&+ If oh &sse$ion "n% 'e"son "$e $ue "n% he 'e"son is !o$$e! e#l"n"ion of he &sse$ion.
two particles is sameQ.27
&sse$ion Two particles are thrown from
same point with different elocity in such a way that ertical component same- The two particle will always lie on a same horizontal line'e"son
.elatie
particles is non zero-
acceleration
of
the
EXERCISE # 3 Q.6
A batsman hits the ball at a height +-0 ft from the ground at pro#ection angle of +2L and the
Q.1
horizontal range is /20 ft- Ball falls on left
f . is the horizontal range and h$ the greatest
boundary line$ where a *+ ft height fence is
height of a pro#ectile$ proe that its initial
situated at a distance of /*0 ft- ,ill the ball clear the fence
*
speed is
*
2(3h + . ) +h
Mg ' 0 m%s* Q.7
*"+ A particle is pro#ected with a elocity of
*9-+ m%s at an angle of 301 to the horizontalind the range on a plane inclined at /01 to the horizontal when pro#ected from a point of the plane up the plane*+ Determine the elocity with which a stone Q.2
A bomb is dropped from a plane flying
must be pro#ected horizontally from a
horizontally with uniform speed- Khow that
point :$ so that it may hit the inclined
the bomb will e"plode ertically below the
plane perpendicularly- The inclination of
plane- s the statement true if the plane flies
the plane with the horizontal is
with uniform speed but not horizontally
h metre aboe the foot of the incline as
θ and : is
shown in the figureQ.3
A stone is thrown horizontally from a towern 0-2 second after the stone began to moe$ the numerical alue of its elocity was -2 times its initial elocity- ind the initial elocity of stone-
Q.4
A shell is fired from a point = at an angle of 301 with a speed of +0 m%s J it stri6es a horizontal plane through =$ at a point A- The
Q.8
A die bomber$ diing at an angle of 2/1 with
gun is fired a second time with the same
the ertical$ releases a bomb at an altitude of
angle of eleation but a different speed - f it
*+00 ft- The bomb hits the ground 2-0 s after
hits the target which starts to rise ertically
being released- (a) ,hat is the speed of the
from A with a constant speed 9 √/ m%s at the
bomber (b) !ow far did the bomb trael
same instant as the shell is fired$ find - (Ta6e g ' 0
horizontally during its flight (c) ,hat were
m%s*)
the horizontal and ertical components of its elocity #ust before stri6ing the ground
Q.5
A cric6et ball thrown from a height of -E m at an angle of /01 with the horizontal at a
Q.9
A boy throws a ball so as to clear a wall of
speed of E m%s is caught by another fieldOs
height PhO at a distance P"O from him- ind
man at a height of 0-3 m from the ground-
minimum speed of the ball to clear the wall-
!ow far were the two men apart
Q.10
During the olcanic eruption chun6s of solid
Q.13
An aeroplane is flying at a height of 930 metre in a horizontal direction with a elocity
roc6 are blasted out of the olcano-
of 00 m%s$ when it is ertically aboe an ob#ect on the ground it drops a bomb- f the bomb reaches the ground at the point N$ then calculate the time ta6en by the bomb to reach the ground and also find the distance NQ.14
A pro#ectile is pro#ected from the base of a hill whose slope is that of right circular cone$ whose a"is is ertical- The pro#ectile grazes the erte" and stri6es the hill again at a point on the base- f θ be the semi&ertical angle of the cone$ h its height u the initial elocity of
(a) At what initial speed would a olcanic
pro#ection and
ob#ect hae to be e#ected at /41 to the
α the angle of pro#ection$
show that
horizontal from the ent A in order to fall
(i) tan θ ' * cot α (ii)
at B as shown in figure-
u* '
(b) ,hat is the time of flight- (g ' 9-E m%s *) Q.11
A boy throws a ball horizontally with a speed
Q.15
gh (+ + tan * θ) *
A person is standing on a truc6 moing with a
of 0 ' * m%s from the Qandhi Ketu bridge C
constant elocity of +-4 m%s on a horizontal
of :atna in an effort to hit the top surface AB
road- The man throws a ball in such a way
of a truc6 traelling directly underneath the
that it returns to the truc6 after the truc6 has
boy on the bridge- f the truc6 maintains a constant speed u ' 2 m%s$ and the ball is
moed 2E-E m- ind the speed and the angle
pro#ected at the instant B on the top of the
of pro#ection (a) as seen from the truc6$ (b) as
truc6 appears at point C$ determine the
seen from the road-
position s where the ball stri6es the top of the truc6-
Q.16
Two bodies are thrown simultaneously from the same point- =ne thrown straight up and the other at an angle
α with the horizontal-
Both the bodies hae e7ual elocity of 0 Neglecting air drag$ find the separation of the particle at time tQ.17
Two particles moe in a uniform graitational field with an acceleration g- At the initial
Q.12
A pro#ectile is pro#ected with an initial elocity of ( 3Hi + EH# ) ms – $ H i ' unit ector
moment the particles were located at one point and moed with elocities / m%s and +
# ' unit ector in in horizontal direction and H
m%s horizontally in opposite directions- ind the distance between the particles at the
ertical upward direction then calculate its
moment when their elocity ectors become
horizontal range$ ma"imum height and time
mutually perpendicular-
of flight-
Q.18
A particle is pro#ected from = at an eleation
α and after t second it has an eleation β as seen from the point of pro#ection- :roe that its initial elocity is
Q.19
gt cos β sin( α – β)
-
* 2
A man running on a horizontal road at E 6m%h finds the rain falling ertically- !e increases his speed to * 6m%h and find that the drops are ma6ing /01 with ertical- ind the speed and direction of the rain with respect to the roadTwo cars A and B haing elocities of 4* 6m%h and E 6m%h are running in the same direction$ the car B being ahead of the A- The distance between the cars is 20 m- f the car A now starts retarding at a uniform rate of m%s* while the car B moes along at a uniform elocity$ will the car A oerta6e the car B
Q.22
Q.24
By how much does the policeman fall%clear the gap (A) clear by 0-09 m (B) miss by 0-09 m (C) clear by 0-20 m (D) miss by 0-9 m
Q.25
The time of flight of policeman to reach the leel of line CD (A) -4E sec (B) *-49 sec (C) 0-23 sec (D) 0-4E* sec
of its elocity when it
is at half its greatest height- ind the angle of pro#ection of the particle-
Q.21
By how much does the thief clear the gap$ if so (A) 0-* m (B) 0-23 m (C) 0- m (D) 0-/ m
The elocity of a particle when it is at its greatest height is
Q.20
Q.23
A pilot is ta6ing his plane towards north with a elocity of 00 6m%h- At that place the wind is blowing with a speed of 30 6m%h from east to west- Calculate the resultant elocity of the plane- !ow far the plane will be after *0 minfrom the starting point
"ss"ge - I *Q. 23 o 25+ A policeman is in pursuit of a thief- Both are running at 2m%s- Kuddenly they come across a gap between buildings as shown in figure- The thief leaps at 2 m%s and at +21 up$ while the policemen leaps horizontally-
"ss"ge - II *Q. 26 o 28+ An eagle is flying horizontally at 0 m%s$ *00 m aboe ground- t was carrying a mouse in its grasp$ which is released at a certain instant- The eagle continues on its path at the same speed for a * sec before attempting to retriee its prey- To catch the mouse it dies in a straight line at constant speed and recaptures the mouse /m aboe the groundQ.26
The time of free fall of mouse is– (A) 3-/+ s (B) /-+ s (C) E-4 s
(D) +-+ s
Q.27
The path length of die of eagle is– (A) 94 m (B) *0-4* m (C) E9 m (D) *-9 m
Q.28
The diing angle of eagle (below horizontal) (A) tan – 3-2/ (B) tan – 3-* (C) tan – 2-/ D) tan – +-2+
"ss"ge III *Ques. 29 o 31+
A particle initially at rest at origin is moing according to law
a '
→
3t H i
+
Et H #
where PaO is accelerationQ.29
elocity of particle at t ' / sec – (A) +2 m%s (B) +0 m%s (C) /2 m%s (D) ** m%s
m%s*$
Q.30
Displacement of particle at t ' / sec – (A) *E m (B) /0 m (C) /2 m (D) +2 m
Q.31
:ath of particle will be – (A) Ktraight line (B) :arabola (C) Circle (D) None
EXERCISE # 4
Q.1
=n a frictionless horizontal surface$ assumed
ume$i!"l )#e Quesion
to be the "&y plane$ a small trolley A is
Q.2
A train is moing along a straight line with a
moing along a straight line parallel to the y&
constant acceleration 5a5- A boy standing in
a"is (see figure) with a constant elocity of
the train throws a ball forward with a speed of
(√/ –) m%s- At a particular instant$ when the
0 m%s$ at an angle of 301 to the horizontal-
line =A ma6es an angle of +2L with the "&
The boy has to moe forward by -2 m
a"is$ a ball is thrown along the surface from
inside the train to catch the ball bac6 at the
the origin =- ts elocity ma6es an angle
initial height- The acceleration of the train$ in
φ with the "&a"is and it hits the trolley-
m%s*$ is-
(a) The motion of the ball is obsered from the frame of the trolley- Calculate the angle φ made by the elocity ector of the ball with the "&a"is in this frame(b) ind the speed of the ball with respect to the surface$ if φ ' +θ %/-
IIT-2002
IIT-2011
EXERCISE # 5(ARCHIVES) Q.3
Two guns$ situated on the top of a hill of height 0 m$ fire one shot each with the same
Q.1
A boat which has a speed of 2 6m%hr in still
speed 2 / ms – at some interal of time-
water crosses a rier of width 6m along the
=ne gun fires horizontally and other fires
shortest possible path in 2 minutes- The
upwards at an angle of 301 with the horizontal- The shots collide in air at a point
elocity of the rier water in 6m%hr is <
:- ind (a) the time&interal between the
IIT-1988
(A)
(B) /
(C) +
(D)
firings$ and (b) the coordinates of the point :Ta6e origin of the coordinate system at the foot of the hill right below the muzzle and
+
tra#ectories in "&y planeQ.2
IIT
1995
Two towers AB and CD are situated a distance PdO apart as shown in figure- AB is *0 m high and CD is /0 m high from the ground-
Q.4
A large$ heay bo" is sliding without friction
An ob#ect of mass m is thrown from the top
down a smooth plane of inclination θ- rom a
of AB horizontally with the elocity of 0
point : on the bottom of the bo"$ a particle is
ms – towards CD- Kimultaneously another
pro#ected inside the bo"- The initial speed of
ob#ect of mass * m is thrown from the top of
the particle with respect to the bo" is u$ and
CD at an angle of 301 to the horizontal
the direction of pro#ection ma6es an angle
towards AB with the same magnitude of
with the bottom as shown in figure-
α
IIT - 1998
initial elocity as that of the first ob#ect- The two ob#ects moe in the same ertical plane$ collide in mid&air and stic6 to each other(a) Calculate the distance between the towers and (b) ind the position where the ob#ects hit the ground-
IIT 1994
(a) ind the distance along the bottom of the bo" between the point of pro#ection : and the point F where the particle lands(Assume that the particle does not hit any other surface of the bo"- Neglect air resistance) (b) f the horizontal displacement of the particle as seen by an obserer on the ground is zero$ find the speed of the bo" with respect to the ground at the instant when particle was pro#ected-
Q.5
The coordinates of a particle moing in a plane are gien by "(t) ' a cos (pt) and y(t) ' b
Q.7
Two particles are pro#ected from the same point with elocities and * ma6ing e7ual
sin (pt) where a$ b (8 a) and p are positie
angle θ ' /01 with the horizontal in opposite
constants of appropriate dimensions- Then –
directions as shown in the figure- ind the
(A) the path of the particle is an ellipse
separation between them when their elocity
(B) the elocity and acceleration of the
ectors become mutually perpendicular- The acceleration due to graity is g-
particle are normal to each other at t ' π%(*p) (C) the acceleration of the particle is always towards a focus (D) the distance traelled by the particle in
Q.8
A pro#ectile is fired with elocity u at an angle θ so as to stri6e a point on the inclined
time interal t ' 0 to t ' π%(*p) is a-
plane inclined at an angle
IIT - 1999
horizontal-
α with the
The point of pro#ection is at a
distance d from the inclined plane on the Q.6
An ob#ect A is 6ept fi"ed at the point " ' / m
ground as shown in the figure- The angle θ is
and y ' -*2 m on a plan6 : raised aboe the
ad#usted in such a way that the pro#ecile can
ground- At time t ' 0 the plan6 starts moing
stri6e the inclined plane in minimum time$
along the G" direction with an acceleration
find that minimum time-
-2
m%s*-
At the same instant a stone is
pro#ected from the origin with a elocity u as shown- A stationary person on the ground obseres the stone hitting the ob#ect during its downwards motion at an angle of +21 to the horizontal- All the motions are in "&y planeind u and the time after which the stone hits the ob#ect- Ta6e g ' 0 m%s *-
IIT 2000
Q.9
A particle is pro#ected with an initial speed u from a point at height h aboe the horizontal plane as shown in the figure-
