Question

A bullet leaves a rifle with a velocity of 200m/s and strikes a wooden target up to 4cm. What velocity it should have to pierce the same block of wood up to 16cm.

Answer 1

When penetrating distance is 4 cm then velocity of bullet = 200 m/sec.

When penetrating distance is 16 cm then velocity of bullet = 4÷200×16 m/sec. = 0.32 m/sec.

Answer 2

Given :

Velocity of bullet , v = 200 m/s .

Distance moved , d = 4 cm = 0.04 m .

To Find :

What velocity it should have to pierce the same block of wood up to 16 cm.

Solution :

Deceleration of bullet :

$v^2-u^2=2as\\\\a=\dfrac{v^2-u^2}{2s}\\a=\dfrac{0^2-200^2}{2\times 0.04}\\\\a=-50000\ m/s^2$

Now , velocity required to pierce the same block of wood up to 16 cm is :

$v^2-u^2=2as\\0-u^2=2\times (-50000)\times 0.16\\\\u=\sqrt{2\times 50000\times 0.16}\\\\u=126.49\ m/s$

Hence , this is the required solution .

Learn More :

Kinematics

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