Question

A bullet bullet moving in horizontal direction, hits the center of the ball. After collision the ball and bullet travel independently. The ball hits the ground at a distance of 20m and the bullet at the distance of 100m from the foot of the post. Find the velocity of the bullet.

A)250m/s
B)250√2 m/s
C)400 m/s
D)500 m/s​

Answer 1

Answer:

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Class 11

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>>A ball of mass 0.2 kg rests on a vertica

Question

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity Vm/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is

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A

250 m/s

B

250

2

m/s

C

400 m/s

D

500 m/s

Hard

JEE Advanced

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Solution

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Correct option is D)

Let the mass of bullet be m and mass of ball be M

initially ball is at height 5m and t rest , the only acceleration is due to gravity

therefore applying equation of motion

S=ut+

2

1

gt

2

5=0+

2

1

(10)t

2

therefore t = 1 sec

so V(ball)=20m/sec

V(bullet) = 100m/sec

So by collision

M×V(ball:final)+m×V(bullet:final)= M×V(boll:initial)+m×V(bullet:initial)

0.01×V(bulletfinal)=0.01×100+0.20×20

V=500m/sec