A bullet is fired on a target with velocity ' V '. Its velocity decreases from ' V ' to ' V/2 ' when it penetrates 30 cm in a target. Through what thickness it will penetrate further in the target before coming to rest? (a) 5 cm (b) 8 cm (c) 10 cm (d) 20 cm

Answer: (c). Constant retardation: drop in v² is proportional to distance. First 30 cm: V² - V²/4 = 3V²/4 = 2a(30) Rest of the way: V²/4 = 2a(x) x/30 = 1/3 ⇒ x = 10 cm So the answer is (c) 10 cm.

A bullet is fired on a target with velocity ' V '. Its velocity… | MHT CET 2023 (11 May, Shift 1)

Q17MHT CET 2023 · 11 MAY · SHIFT 1Medium

Equations of Kinematics

A bullet is fired on a target with velocity ' $V$ '. Its velocity decreases from ' $V$ ' to ' $V/2$ ' when it penetrates $30\text{ cm}$ in a target. Through what thickness it will penetrate further in the target before coming to rest?

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Answer: (c)

Constant retardation: drop in $v^2$ is proportional to distance.
First 30 cm: $V^2 - \frac{V^2}{4} = \frac{3V^2}{4} = 2a(30)$
Rest of the way: $\frac{V^2}{4} = 2a(x)$
$\frac{x}{30} = \frac{1}{3} \Rightarrow x = 10\text{ cm}$
So the answer is (c) 10 cm.

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