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A bullet is fired into a wooden piece in the wall with a certain velocity. The bullet pierces into the wooden piece at a distance of $10 cm$ . If the bullet has a retardation of $50 km / s^{2}$ , then the velocity of the bullet is [[1]] $m / s$ .

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Detailed Solution

A bullet is fired into a wooden piece in the wall with a certain velocity. The bullet pierces into the wooden piece at a distance of

10 cm

. If the bullet has a retardation of

50 km / s^{2}

, then the velocity of the bullet is

100 m / s .

Given that,
Retardation of the bullet

r = 50 km / s^{2}

\Rightarrow

= 50000 m / s^{2}

(As

1 km = 1000 m

)
Therefore,

acceleration (a) = - 50000 m / s^{2}

Distance travelled by the bullet,

s = 10 cm

\Rightarrow

= 0.1 m

The bullet's final velocity is

v = 0

Using third equation of motion,

v^{2} - u^{2} = 2 as

Where,

v = final velocity

u = initial velocity

a = acceleration

s = distance covered

0 - u^{2} = 2 \times - 50000 \times 0.1

u = \sqrt{10000} m / s

\Rightarrow u = 100 m / s

Therefore, initial velocity of bullet is

100 m / s

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