A bullet fired into a fixed target loses half of its velocity after penetrating 3cm. How much further will it penetrate before coming to rest assuming that it faces constant resistance to motion?
A
1.5cm
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B
1.0cm
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C
3.0cm
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D
2.0cm
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Solution
The correct option is B1.0cm Let initial velocity of the bullet =u After penetrating 3cm its velocity becomes u2 From v2=u2−2as (assuming constant deceleration a) (u2)2=u2−2a(3) ⇒6a=3u24⇒a=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)2−2as ⇒0=(u2)2−2(u28).x ⇒x=1cm