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Question

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further will it penetrate before coming to rest assuming that it faces constant resistance to motion?

A
1.5 cm
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B
1.0 cm
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C
3.0 cm
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D
2.0 cm
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Solution

The correct option is B 1.0 cm
Let initial velocity of the bullet =u
After penetrating 3 cm its velocity becomes u2
From v2=u22as (assuming constant deceleration a)
(u2)2=u22a(3)
6a=3u24a=u28
Let it further penetrate through distance x and stop at point C.
From B to C,
Final velocity=0, Intial velocity =u/2, s=x,a=u2/8
So,
v2=(u2)22as
0=(u2)22(u28).x
x=1 cm

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