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

I got this question in an interview for job.

The above asked question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

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.