# A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?

Category: QuestionsA bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?
Editor">Editor Staff asked 11 months ago

A bullet fired into a target loses half of its velocity after penetrating 2.5 cm. How much further will it penetrate?

(a) 0.85 cm

(b) 0.84 cm

(c) 0.83 cm

(d) 0.82 cm

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The above asked question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12
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Editor">Editor Staff answered 11 months ago

The correct option is (c) 0.83 cm

Best explanation: Let, u cm/sec be the initial velocity of the bullet.

By the question, the velocity of the bullet after pertaining 2.5 cm into the target will be u/2 cm/sec.

Now if the uniform retardation to penetration be f cm/sec^2,

Then using the formula, v^2 = u^2 – 2fs, we get,

(u/2)^2 = u^2 – 2f(2.5)

Or f = 3u^2/20

Now let us assume that the bullet can penetrate x cm into the target.

Then the final velocity of the bullet will be zero after penetrating x cm into the target.

Hence, using formula v^2 = u^2 – 2fs we get,

0 = u^2 – 2(3u^2/20)(x)

Or 10 – 3x = 0

Or x = 10/3 = 3.33(approx).

Therefore, the required further penetration into the target will be

3.33 – 2.5 = 0.83 cm.