Question

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A bullet moving with a velocity of
50\sqrt{2} \frac{m}{s}50
2
​

s
m
​

is fired into a target which it penetrates to the extent of
dd
metre. If this bullet is fired into a target of
\frac{d}{2}
2
d
​

metre thickness with the same velocity, it will come out of this target with a velocity of [Assume that resistance to motion is similar and uniform in both the cases]

Answers:-

a)
40 \sqrt{2} \frac{m}{s}40
2
​

s
m
​

b)
25 \sqrt{ 2 } \frac{m}{s}25
2
​

s
m
​

c)
50 \frac{m}{s}50
s
m
​

d)

5.0 \sqrt{3}5.0
3
​

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Answer 1

We have the mass of bullet m1 = 20 g (= 0.02kg) and the mass of the pistol, m2 = 2kg; initial velocities of the bullet (u1) and pistol (u2) = 0 respectively. The final velocity of the bullet, v1 = + 150m s -1. The direction of bullet is taken from left to right(positive,by convention). Let v be the recoil velocity of the pistol
Total momenta of the pistol and bullet before the fire when the gun is at rest
= (2+0.02)kg * 0m s -1
= 0kg m s -1
Total momenta of the pistol and bullet after it is fired
= 0.02 kg * (+150 m s -1)+2kg *v m s-1
= (3 + 2v) kg m s-1
According to the law of conservation of momentum
Total momenta after the fire = Total momenta before the fire
3+2v = 0
=> v = -1.5 m s-1.
Negative signs indicates that the direction in which the pistol would recoil is opposite to that bullet that is right to left.
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