ANDHERI / BORIVALI / DADAR / THANE / POWAI / CHEMBUR / NERUL / KHARGHAR
IIT – JEE
ASSINGMENT
DATE:
TOPIC: KINEMATICS
1.
Four Four rods rods each each of leng length th l have have been been hing hinged ed to to form form a rhomb rhombus. us. Vertex A is fixe fixed d to a rigid rigid suppor support, t, vertex C being pulled to the right along x-axis with a uniform speed v as shown in fig. The speed with which vertex moves toward C at the moment the rhombus ta!es the shape of a s"uare is
v
#A$ &.
%
#$
&
#C$
&
#'$ v
A pro( pro(ec ecti tile le is thr throw own n wit with h a vel veloc ocit it) ) of of 1* 1* m+s m+s at at the the angl anglee of of * * o with the horiontal. The interval between moments when speed is g m+s is #g / 1* m+s&$ #A$ % s
0.
v
v
#$ 0 s
#C$ & s
#'$ 1 s
A (uggler !eeps balls going up within one hand, so that at an) instant, % balls are in air and one ball in the hand. f each ball rises to a height of &* m, then the time for which each ball sta)s in the hand & g = 1* m + s ) ( is#A$ 1.* s #$ 1. s #C$ &.* s #'$ %.* s
%.
A ball is dropped from the 2 th store) of a multistoried building. n the first second of free fall another ball is dropped from the 3th store) 1 m below the 2 th store). f both the balls reach same time, then g = 1* m + s & ) ( height of the building is#A$ 1* m #$ 1 m #C$ &* m #'$ & m
.
Two boats boats,, a and and b, move move wit with h cons constan tantt velo veloci citie tiess m+s m+s and and 1* 1* m+s m+s alo along ng two two mut mutua uall) ll) perpendicular straight trac!s toward the intersection point of the two trac!s 4. At the moment t / *, the boats were located at distances, 1* m and &** m from 4. The shortest distance, between the boats, would be #nearl)$ #A$ m #$ *m #C$ &m #'$ *m
α x & α β . The tim time is expr expres esse sed d as func functi tio on of x wher wheree and are constants as t / The ratio of retardation to acceleration isvelocit). #A$ 3.
&α v0
#$ 1
#C$ 51
+ β x and
v is
#'$ 6ero
A (et air plane plane trav travelli elling ng at a speed speed of of ** ** !m+h !m+h e(ect e(ectss its its produ products cts of comb combust ustion ion #gases$ #gases$ which which appear at a speed of 1** !m+h, relative to the (et plane. 7hat is the velocit) of latter with respect to the ground8 #A$ 1*** !m+h along the direction of emission of gases
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:.
2.
#$ &*** !m+h along the direction of emission of gases #C$ 1*** !m+h opposite to the direction of emission of gases #'$ &*** !m+h opposite to the direction of emission of gases A river is flowing from west to east at a speed of m+min. A man on the south ban! of the river, capable of swimming at 1* m+min in still water, wants to swim across the river in the shortest time. ;e should swim in a direction. #A$ 0** west of north #$ 0** east of north #C$ due north #'$ ** east of north Two stones are thrown up simultaneousl) with initial speed of u1 and u& #u&< u1$. The) hit the ground x1$, their after s and 1*s respectivel). 7hich graph correctl) represents the variation of ∆ x / # x& 5 relative separation with time up to t / 1* s8 Assume that the stones do not rebound after hitting the ground. #A #$ $
#C$
1*.
An elevator car whose floor to ceiling distance is &.3 m starts ascending with a constant acceleration of 1.& m+s &. & seconds after the start, a bolt falls from the ceiling of the car. The free fall time of the bolt is #g/2.:m+s&$ #A$
11.
1&.
#'$
&.3 s 2.:
#$
.% s 2.:
#C$
.% s :.
#'$
.% s 11
A particle is moving eastwards with a velocit) of m+s. n 1& second the velocit) changes to m+s northwards. The average acceleration in this time is 1 1 #A$
& m+s& toward north-east
#$
& m+s& toward north-west
#C$
& m+s& toward north-east
#'$
& m+s& toward north-west
A rod of length l slides down along the inclined wall as shown in fig. At the instant shown in figure, the speed of the end A is v, then the speed of will be
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V #A$
10.
f
cos φ
V
cos θ
A1 = A &
#$
cos θ
V
cos φ
#C$
sin φ
V
sin θ
#'$
A1
are two non 5 collinear unit vectors and if
+A =
sin θ sin φ
0
&
, then the value of
( A − A ) . ( &A + A ) is 1
&
1
&
1
#A$ 1 1%.
#$
0
&
#C$
&
The magnitudes of x and ) component of A are 3 and . The magnitudes of x and ) component of
A + B are 11 and & respectivel) then the magnitude of B is #A$ #$ #C$ : 1.
gR
#A$ gcosθ
13.
#'$ 2
A frictionless wire A fixed on a sphere of radius >. A ver) small spherical ball slips on this wire. The time ta!en b) this ball to slip from A to is
&
1.
#'$ &
& gR #$
cosθ g
#C$
g
R
&
g
#'$
gR cosθ
& A roc!et is fired verticall) upwards and moves with net vertical acceleration of &* m + s . After 1 minute the fuel is exhausted. The time ta!en b) it to reach the highest point after the fuel is exhausted will be nearl) #g / 1* m+s &$ #A$ % min #$ & min #C$ 1 min #'$ *. min
A bod) is pro(ected with velocit) v1 from the point A as shown in the figure. At the same ti me, another bod) is pro(ected verticall) upwards from with the velocit) v &. The point lies verticall) V 1 below the highest points. For both the bodies to collide, should be V 2
0 #A$ & 1:.
#$ *.
#C$
&
#'$ 1
v =& v = :t 5 & A particle moves in the x 5 ) plane with velocit) x and y . f it passes through the point x / 1% and ) / % at t / & s then the e"uation of the path is 0 & & X y 5 y & X y 5 y +& = + = #A$ #$
#C$ X
=
y0 5 0 y
+&
#'$ X
=
y0 5 & y & + &
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12.
A man is moving with velocit) u in north east direction. The wind appears to blow from the north to the moving man. 7hen the man doubles his velocit), the wind appears to move in the dire ction cot -1 #&$ east of north. The actual velocit) of the wind is v v #A$
&
towards east
#$
&
#C$
& v towards west
#'$
& v towards east
towards west
&*.
The speed of boat is !m+h in still water. t crosses a #flowing$ river of width 1 !m along the shortest possible path in 1 minutes. The velocit) of river is #A$ % !m+h #$ 0 !m+h #C$ 1 !m+h #'$ .2% !m+h
&1.
The motor of an electric train can give it an acceleration of 1m+s& and brea! can give a negative acceleration of 0 m+s&. The shortest time in which the train can ma!e a trip between the two station 1&1 m apart is #A$ 110. s #$ .2 s #C$ * s #'$ s
&&.
A &m wide truc! is moving with a uniform speed : m+s along a horiontal road. A pedestrian starts to cross the road with a uniform speed ϑ when the truc! is % m awa) from him. The minimum value ϑ so that he can cross the road safel) is#A$ 1.%1% m+s #$ &.& m+s #C$ 0.3 m+s #'$ %.* m+s
of
&0.
An open elevator is ascending with constant speed of 1* m+s. A ball is thrown verticall) up b) a bo) on elevator when it is at a height of %* m from the ground. The velocit) of pro(ection with respect to the elevator is 0* m+s. The maximum height attained b) the ball is-#g/1* m+s &$ #A$ : m #$ * m #C$ 1&* m #'$ % m
&%.
A bod) is pro(ected with velocit) V1 from the point A as shown in the figure. At the same time, another bod) is pro(ected verticall) upwards from with the velocit) V &. The point lies verticall) V 1 below the highest points. For both the bodies to collide, should be V 2
0 #A$ &
#$ *.
#C$
&
#'$ 1
&.
From the top of a tower of height of * m a ball is thrown verticall) upwards with a certain velocit). t hits the ground in 1* s after it is thrown up. ;ow much time does it ta!e to reach from A to , where A and are two points &* m and %* m below the edge of the tower8 #A$ &.* s #$ 1.* s #C$ *. s #'$ *.% s
&.
Two particles start from the same point with different speeds. 4ne particle moves along )/a sin wx and other moves along ) / a cos wx. 7hich of the following statements is true8 #A$ The) never collide with each other. #$ The) must collide after some time. π , a %w &÷ #C$ The) ma) collide at a point ? π a # , $ & w & #'$ The) ma) collide at a point ?
&3.
A bod) moves along x-axis with velocit) v. f the plot v-x is an ellipse with ma(or axis &A and minor axis &V*, the magnitude of maximum acceleration is & & V* A& V* A A + V * V* + A #A$ #$ #C$ #'$
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&:.
A police Van moving on a highwa) with a speed of 0 !m+h fires a bullet at a thief@s car speeding awa) in the same direction with a speed of &1 !m+h. f the mule speed of the bullet is 1* m+s, with what speed does the bullet hits the thief car8 #A$ :* m+s #$ 1** m+s #C$ 1&* m+s #'$ 1* m+s
&2.
A boat, going down stream, crosses a drifting raft at a point ?. After two hours, the boat, it turned bac! and after some time, passed the same raft again at a distance 1& !m from the point ?. Assuming that the speed of the river, remains constant, the value of boat@s speed, is #A$ % !m+h #$ 0 !m+h #C$ 6ero #'$ 1 !m+h
0*.
>am is going eastward with a velocit) of % !m+h. The wind appears to blow directl) from the north. ;e doubled his speed and the wind appears to come from north east. The actual velocit) of the wind is
01.
−1 #A$ % &km + h towards north east
−1 #$ % &km + h towards north west
−1 #C$ % &km + h towards south west
−1 #'$ % &km + h towards south east
Two stones are thrown verticall) up, simultaneousl), with initial speeds of u1 / 1 m+s and u & / 0* m+s, from the edge of a cliff of height &** m. Ta!e g ∼ 1* m+s& and assume that the stones do not rebound when the) hit the ground. The graph, representing the relative vertical separation, between the two stones, as a function of time, would be the graph labeled as graph #A #$ $
#C$
#'$
0&.
A car driver, travelling at 2* !m+h sees the light turn red at the intersection. f her reaction time is *.s, and the car can decelerate at m+s &. The stopping distance for the car would be #A$ 2. m #$ &. m #C$ :. m #'$ 33. m
00.
A car and a truc!, start moving #from rest$ along the same straight trac!, at the same instant of time, from the same point. The car moves with a constant velocit) of * m+s and the truc! moves with a constant acceleration of % m+s &. The separation, between the two, will have it greatest value #/ s* metre, sa)$, at a time t*, after the start, where t* and s * e"ual, respectivel). #A$ 1&. s and & m #$ & s and 01&. m #C$ 1&. s and 01&. m #'$ & s and & m
0%.
Three persons ?, and > of same mass travel with same speed u along an e"uilateral triangle of side Bd@ such that each one faces the other alwa)s. After how much time the) will meet each other-
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%
#A$
0.
&d
&d
d #$
0u
A bird flies for %s with a velocit) of distance of #A$ : m #$ m
#C$
t − & ms −1
d
0u
#'$
0u
in a straight line, where t / time in second. t covers a
#C$ % m
#'$ & m
0.
?article A and are both moving along the x-axis. At time t / *, A has a velocit) of 1* m+s and an acceleration of -% m+s&. ?article has a velocit) of &* m+s and an acceleration of -&m+s &. nitiall) both the particles are at the origin - at time t / & s, distance between the two particles is, #A$ &% m #$ -0& m #C$ -1 m #'$ 1 m
03.
7hat are the speeds of two ob(ects if #i$ when the) move uniforml) towards each other, the) get % m closer in each second, and #ii$ when the) move uniforml) in the same direction, with their original speeds, the) get %m closer to each other after 1*s8 #A$ %.% m+s and 0. m+s #$ 0.0 m+s and &.3 m+s #C$ %.% m+s and &.& m+s #'$ &.& m+s and 1.: m+s
0:.
The motor of an electric train can give it an acceleration of 1m+s& and its bra!es can give it a negative acceleration of 0 m+s&. The shortest time in which the train, can ma!e a trip between the two stations, 1&1 m apart is #A$ 110. s #$ .2 s #C$ * s #'$ s
02.
A &m wide truc! is moving with a uniform speed : m+s along a horiontal road. A pedestrian starts to cross the road with a uniform speed ϑ when the truc! is % m awa) from him. The minimum value ϑ so that he can cross the road safel), is #A$ 1.%1% m+s #$ &.& m+s #C$ 0.3 m+s #'$ %.* m+s
of
%*.
,
A boat which has a speed of 1* !m+h in still water crosses a river of width & !m along the shortest possible path in 1 min. The velocit) of the river water in m+min is #A$ .
#$ 1.
#C$ 1**
#'$
%1
%1.
7hat will be the speeds of two ob(ects if, when the) move uniforml) towards each other, the) get m closer in each second and when the) move uniforml) in the same direction with original speeds, the) get m closer each seconds8 #A$ 0. m+s and &.% m+s #$ 0.& m+s and &.1 m+s #C$ %.& m+s and 0.: m+s #'$ 0.* m+s and &.& m+s
%&.
Two balls are hold separated b) 1*. m verticall) one above the other. The) are released simultaneousl) to fall freel) under gravit). After 0 seconds the relative separation between them will be #A$ .1 m #$ 02. m #C$ &&.m #'$ 1*. m
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%0.
A swimmer crosses a river of width d flowing at velocit) v. 7hile swimming, he heads himself alwa)s at an angle of 1&* * with the river flow and on reaching the other end he finds a drift of d+0 in the direction of flow of river. The speed of swimmer with respect to the river is
(
, 0
#A$
−
0
)v
#$
( 0− 0) v
#C$
( 0 + 0) v
(
& 0
#'$
−
0v
)
%%.
A train is moving slowl) on a straight trac! with a constant speed of m+s. A passenger in that train starts wal!ing at a stead) speed of m+s to the bac! of the train in the opposite direction of motion of the train. Do to an observer standing on the platform directl) in front of that passenger, the velocit) of the passenger appears to be #A$ 1* ms 51 #$ ms 51 in the same direction to the train #C$ ero #'$ ms 51 in the opposite direction to the train
%.
To a man wal!ing at the rate of !m+h the rain appears to fall verticall). 7hen he increases his speed to 1* !m+h it appears to meet him at an angle of % * with vertical. The actual speed of rain is #A$ 0 !m+h
#$
&
!m+h
#C$
1*
&
!m+h
#'$
3 !m+h
%.
An air craft flies at * !m+h in still air. A wind of &* & !m+h is blowing from south. The pilot wishes to travel from pt A to north-east of A. The direction he must steer if distance A / 1*& !m is #A$ %* from D towards 7 #$ 1&** from E towards 7 #C$ ** from D towards #'$ 3* from E towards
%3.
A swimmer crosses a river &** m wide in minimum time of 1* min with a drift of 1&* m. f he crosses the river ta!ing shortest path, he ta!es 1&. min. The velocit) of the swimmer in still water s
#A$ 1& m+min %:.
#$ 1: m+min
#C$ &* m+min
#'$ 1& m+sec.
oat A is located % !m north and 0 !m east of oat . oat A has a velocit) of &* !m+h towards the south and boat is moving at %* !m+h in a direction 03 * north of east. G and H axes are along east and north direction respectivel). $ $ Velocit) of A relative to is 0&i − %% j #A$ r = ( 0 5 0&t ) $ i + ( % − %%t ) Ij ?osition of A relative to as a function of time is given b) AB #$ $ $ #C$ Velocit) of A relative to is 0&i + %% j $ $ ?osition of A relative to as a function of time is given b) 0&t i − %%t j #'$
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%2.
A man standing at position A on the ban! of river as shown in given figure notices that a child is in danger at position across the river. The speeds at which he can swim and wal! are V 1 and V& respectivel). The condition for minimum time of travel is.
Cos θ 1
#A$ *.
Cos θ &
v&
#$
tan θ &
=
sin θ 1
v1 v&
#C$
sin θ &
=
sec θ 1
v1 v&
sec θ &
#'$
=
v1 v&
A man standing on the side of a road finds a car approaching with speed JuJ on his side of the road. Kndeterred, he starts crossing the road with speed JvJ at a time when the distance of the car from him is J l J. The angle θ , the man must ma!e with the edge of the road to minimie the danger is
θ = cot
−1
#A$ 1.
v ÷ u
θ = sin #$
−1
v u÷
θ = cos #C$
−1
v u÷
θ = cos−1
#'$
v
÷
u÷
A tiger charges directl) towards a hunter with a constant speed of 1 m+s. At the instant the tiger is 1** m awa), the hunter fires an arrow at 0*L with the horiontal. The initial speed of the arrow if it is to stri!e the target should be −1 #A$ &.&ms
&.
tan θ 1
v1
=
#$
&,.1+
& ms
−1
#C$
− #'$ &.1ms
1
&,.1 0 + &
Two particles have been pro(ected under gravit) horiontall) in two opposite directions from the same height with speed J u1J ='u&J as shown. The separation between them when the) are moving perpendicularl) is
#A$ u1 − u&
u1u & + g
#$
u1 u& + g
#C$
( u + u ) u u + g 1
&
1
&
#'$
u1u& + g
0.
A bird flies for :s with a velocit) of Mt5%M m+s in straight line, where t / time in seconds. t covers a distance of #A$ 1m #$ :m #C$ %m #'$ &m
%.
A particle starts from rest. n JaJ vs time graph as shown in the figure, the maximum speed of the particle will be
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#A$ 12m+s .
#C$ 3:m+s
#'$ 1m+s
f the velocit) v of a particle moving along a straight line decreases linearl) with its displacement from %*m+s to a value approaching ero at s / %*m, then acceleration of the particle at v / &*m+s is
#A$ 5%* m+s& .
#$ 02m+s
#$ 5&* m+s&
#C$ 51* m+s&
#'$ 5m+s&
A stationar) man observes that the rain is falling verticall) downward. 7hen he starts running with a velocit) of 1!m+h, he observes that the rain is falling at an angle of % * with the vertical. The actual velocit) of the rain is #A$ 1* !m+h
#$
1 0
!m+h
#C$ 1 !m+h
#'$
1 & !m+h
3.
A person wal!s up a stalled escalator in 1&* second. 7hen (ust standing on the same moving escalator, he is carried in 2* second. The time it would ta!e him to wal! up the moving escalator is #A$ 0*.** s #$ %*.: s #C$ 1.%& s #'$ &1*.** s
:.
f a particle ta!es JtJ second less and ac"uires a velocit) of JvJ m+s more in falling through the same distance on two planets, where the acceleration due to gravit) are %g and 1g, respectivel) then #A$ v / >
2.
#$ v / %gt
#C$ v /
& gt
#'$ v /
: gt
A pro(ectile is moving with speed * m+s at its highest point, where it brea!s into two e"ual parts due to internal explosion. 4ne part moves verticall) up at * m+s with respect to ground. The other part will move with −1 #A$ 10 √ 61 #$ 110 #C$ 120 #'$ 10* ms
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ANSWER KEY
1.
(C)
. 11. 1. &1. &. 01.
(C) (B) (B) (B) (A) (A) (A)
0. %1. %. 1. .
(A) (D) (D) (C)
&. 3.
(D) (A)
0. :.
(A) (C)
%. 2.
(C) (A)
. 1*.
(A) (D)
1&. 13. &&. &3. 0&. 03.
(B) (B) (C) (C) (D) (D)
10. 1:. &0. &:. 00. 0:.
(B) (B) (C) (B) (C) (B)
1%. 12. &%. &2. 0%. 02.
(A) (A) (B) (A) (B) (C)
1. &*. &. 0*. 0. %*.
(C) (B) (D) (D) (C) (C)
%&. %3. &. 3.
(D) (C) (C) (C)
%0. %:. 0. :.
(B) (B) (A) (B)
%%. %2. %. 2.
(C) (A) (C) (D)
%. *. .
(B) (C) (B)
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