d.
FIITJEE – Bhilai Bhilai Centre CPP 6
its entire journey (till it reaches the ground)
TOPIC: 2-D and Projectile Motion 1.
The co-ordinates of a particle undergoing a 2-D motion varies with time as 3
Average speed and average velocity of the ball over
e.
Time when its speed becomes half of its projection speed.
2.
A batsman standing at ‘A’ hits the ball towards the o
2
bowler (standing at B) at an angle of 60 with the
2
x = t -2t and y = -2t -2t + t +1
horizontal with speed of 20m/s. The length of the pitch
a.
the time when it crosses x-axis
(AB) is 10 m. find the speed with which the bowler
b.
the time when it crosses y-axis
should run so as to catch the ball just before it touches
c.
speed at t=5 sec
the ground.
d.
Average
velocity
and
average
acceleration
between the times t 1 and t2 if t 1 and t 2 are the time at which x-component of velocity is double of the y-component of the velocity. e.
2.
Average velocity in the interval when a x
A particle moves in x-y plane with velocity Vx=8t-2 and Vy=2. If it passes through the point x=14 and y=2 at t=2
sec, then the equation of the path is
3.
2
a.
x = y -y+2
b.
x = y -2
c.
x = y +y-6
d.
None of these
3.
and acceleration are
2
a) parallel to each other
2
b) Anti parallel to each other c) Inclined to each other an angle of 45
The horizontal and vertical displacement of a particle moving along a curved line are given by x=5t and y=2t2+t. Time after which its velocity vector makes an
4.
4.
c. 2 sec
d. 1.5 sec
The height y and distance x along the horizontal plane
a) 37.5m b) 22.5m c) 90m d) 11.25m 5.
in seconds. The velocity of projection is
a) 125m b) 50m c) 100m d) 150m 6.
projectile at any time ‘t’ is ‘h’ then H/h is () ) 2 a) (T/t) b) T/t c) d)
The acceleration of the particle moving in x-y plane is
⃗=̂ ̂ ms-2 Initially the particle is at (100m, -200m) and its initial -1 velocity is ms
7.
A ball is projected with a velocity 20m/s at an angle to the horizontal. In order to have maximum range, its
Choose the correct statements
velocity at the highest point must be
a.
The particle crosses the x-axis at t=12 sec
b.
The particle will never cross x-axis
c.
The particle will touch y-axis at t=10 sec
maximum horizontal distance that a ball thrown
d.
The particle will pass through origin The average velocity in first five seconds is
with a speed of 40 m/s can go without hitting the
e.
̂̂ ̂ ̂
a) 10m/s b) 14m/s c) 16m/s d) 18m/s 8.
9.
40√ m/s at 45 . Find
A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground
A projectile is projected from ground with a velocity o
The ceiling of a long hall is 25m high. What is the
ceiling of the hall?
Projectile Motion 1.
The maximum height reached by the projectile is h. Time taken to reach the maximum height is T. If height of the
a. 8 m/s b. 6 m/s c. 10 m/s d. Data insufficient 5.
If the time of flight of a projectile is 10 s and range is 500m, then the maximum height attained by it is
of a projectile on a certain planet (with no atmosphere) 2 are given by y=(8t-5t ) meter and x=6t meter where t is
A stone is projected in air. Its time of flight is 3s and range is 150m. Maximum height reached by the stone is
o
b. 1 sec
o
d) Perpendicular to each other
angle of 45 with the horizontal is a. 0.5 sec
At the top of the projectile, the directions of its velocity
can the cricketer throw the same ball? 10.
Two bodies are thrown with the same initial velocity at
Velocity and displacement of particle at 2 sec.
angles θ and 9090-θ with the horizontal. Their maximum
b.
Direction of travel of the ball at 2 sec.
heights are in the ratio
c.
Angle between the velocities at t = 2 sec and t = 6
a.
sec.
2
2
a) 1:1 b) sinθ:cosθ c) sin θ:cos θ d) cosθ: sinθ
11.
If T1 and T2 are the time of flights for two projections
moving horizontally. What is the velocity of projection
with same initial velocity and complementary angles of
of the ball? a) √ √ m b)
projection, then the range of the projectile is given by a) R=4gT1T2
12.
b) R=2gT1T2
c) R=(gT1T2)/2
d)
22.
If two projectiles have same initial speed and range but
hole in B is 10cm below the hole in A. If the bullet is
different angles of projection and H 1 and H 2 are their
travelling horizontally at the time of hitting A, then
max
the velocity of the bullet at A is a) 100 m/s b) 200 m/s c) 600 m/s d) 700 m/s
b) c) d)
23.
A projectile is thrown with a velocity u making an angle θ with vertical. It just crosses the top of two poles each of
Three balls of same masses are projected with equal speeds at angle of 15 , 45 , 70 and their ranges are R 1,
height h after 1s and 3s respectively. The maximum height
R2 and R 3 respectively. Then
of the projectile is
o
o
o
a) 10m
a) R1 > R2 > R3
b) R1 < R2 < R3
c) R2 > R1 > R3
d) R2 > R3 > R1
24.
b) 20m
c) 40m
d) 5m
A package is dropped from an airplane horizontally with
A projectile has a range R and time of flight T. If the
an initial velocity 10m/s from a height of 20m. If wind is
range is doubled (by increasing the speed of projection
imparting a horizontal acceleration of 0.1m/s , then at
without changing the angle of projection), the time of
what horizontal distance x from the point of dropping,
flight will become
should
a) √ √ 15.
Two paper screens A and B are separated by a distance of 100m. A bullet pierces A and then B. The
a)
14.
m c) √ √ m d)√ √ m
R=(gT1T2)/4
heights, then their range is
13.
√ √
b√
c) T/2
2
the
pickup
person
stand?
d) 2T
The total speed (V t) of the projectile at its greatest height is
of its total speed when it is at half of its
greatest height. What is the angle of projection? 16.
A ball is projected from the ground with a speed of o
20m/s at an angle of 45 with horizontal. There is a wall of 25m height at a distance of 10m from the point of projection. The ball will hit the wall at a height of a) 5m b) 7.5m c) 10m d) 12.5m 17.
Multiple correct
At time t=0, a ball is projected from point A with a o
velocity of 60m/s at 60 angle with horizontal.
25.
o
of the ball makes an angle of ± 45 with the horizontal
horizontal). Let R 1 and R2 be their horizontal ranges,
axis.
H1 and H2 their maximum heights and T 1 and T2 are
o
their time of flights. Then a) b) c)
A ball is projected vertically upwards from the top of a tower with a velocity 50m/s making an angle o
of 30 with the horizontal. The height of the tower is 70m. After how many seconds from the instant
26.
a) 2 s
b)
5 s c) 7s
20.
A ball if thrown from the ground to clear the wall 3m high at a distance of 6m and falls 18m away
21.
A particle is projected from ground with velocity 40 √
b) Vertical component of the velocity is 20m/s c) Velocity makes an angle of with vertical d) Particle is at a height of 60m from ground
ground is m c) √ m d)√ m
a) Displacement of the particle is 100m
d) 9s
covered by the projectile before reaching the
√
d)
o
In the above problem, the horizontal distance
a) √ m b)
m/s at 45 . At time 2 sec
of throwing, will the ball reach the ground? 19.
o
initial velocities at angles 60 and 30 (with
Determine the two times t1 and t2 when the velocity
18.
Two particles are projected from ground with same
27.
At a height of 15m from the ground, velocity of a projectile is
=̂ ̂ ̂ ̂ . Here ̂ is vertically upwards
and ̂ is is along horizontal direction and g=10m/s , then 2
o
from the wall. Find the angle of projection of ball.
a) Particle was projected at an angle of 45 with
A ball is projected from the ground at an angle θ
horizontal
with the horizontal. After 1 second it is moving at
b) Time of flight of projectile is 4s
an angle of 45o with the horizontal and after 2 s it is
c) Horizontal range of projectile is 100m d) Maximum height of projectile from ground is 20