Question

A man shot a bullet with a speed of 10 m s-¹ which just penetrates a plank of wood. With what speed should he
shoot the bullet so that it passes through 10 similar planks?
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Answer 1

Step by step Explanation:

Given:A man shot a bullet with a speed of 10 m s-¹ which just penetrates a plank of wood.

To find: With what speed should he shoot the bullet so that it passes through 10 similar planks?

Solution:

We know that kinetic energy of bullet is given by 1/2 mv²

Speed (v) = 10 m s-¹

$E = \frac{1}{2} m {v}^{2} \\ \\ E = \frac{1}{2} m( {10)}^{2} \\ \\ E = \frac{1}{2} m \times 100 \\ \\ E = 50m$

Energy required to penetrate 10 such plank of wood.

$E' =10 \times 50 \: m \\ \\ E' = 500 \: m$

New velocity(v'):

$500 \: m = \frac{1}{2} \: m \: {v'}^{2} \\ \\ {v'}^{2} = 1000 \\ \\ v' = \sqrt{1000} \\ \\ v'= 10 \sqrt{10} \: m {s}^{ - 1}$

Final answer:

New velocity should be

$\bold{\red{v' = 10 \sqrt{10} \: m {s}^{ - 1}}}$

Hope it helps you.

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