Question

A bullet fired into a wooden block loses half of its velocity after penetrating 9 cm. It comes to rest after penetrating a further distance of

Answer 1

Answer:

The correct answer is : 40/3 cm.

Explanation: Here is the explanation-

(from A to B)

v2 = u2 – 2as

⇒ (v/2)2 = v2 – 2a x 40

v2/4 – v2 = -80a

⇒ a = 3v2/320

(from B to C)

v2 = u2 – 2as

⇒ 0 = (v/2)2 – 2 x (3v2/320) x X

⇒ X = (40/3) cm

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Answer 2

Given

$\text { For first part of penetration, by equation of motion }$

$\left(\frac{u}{2}\right)^{2}-(u)^{2}=2 a S \text { or } a=-\frac{3 u^{2}}{8 S} . . \text { (i) }$

$\text { For later part of penetration }$

$(0)^{2}-\left(\frac{u}{2}\right)^{2}=2 a S^{\prime} \text { or } S^{\prime}=-\frac{u^{2}}{8} a$

$S^{\prime}=\frac{u^{2}}{8} \frac{8 S}{-3 u^{2}}(\text { Using (i)) }$

$S^{\prime}=\frac{S}{3}=\frac{9}{3} \mathrm{~cm}(\mathrm{~S}=9 \mathrm{~cm} \text { given })$

$The answer is S^{\prime}=3$