Question

a bullet with velocity 200m/s strikes a wooden block and pierce it till 10cm find its retardation
​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Retardation=200000\:m/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Velocity \: of \: bullet(u) = 200 \: m/s \\ \\ \tt: \implies Pierce \: length(s) = 10 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Retardation \: of \: bullet(r) = ?$

• According to given question :

$\tt \circ \: Final \: velocity = 0 \: m/s \\ \\ \tt \circ \: Pierce \: length = \frac{10}{100} = 0.1 \: m \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies {v}^{2} = {u}^{2} + 2as \\ \\ \tt: \implies {0}^{2} = {200}^{2} + 2 \times a \times 0.1 \\ \\ \tt: \implies 0 = 40000 + 0.2 \times a \\ \\ \tt: \implies - 40000 = 0.2 \times a \\ \\ \tt: \implies a = \frac{ - 40000}{0.2} \\ \\ \green{\tt: \implies a = - 200000 \: m/s^{2} } \\ \\ \green{\tt \therefore Retardation \: of \: bullet \: is \: 200000 \: m/{s}^{2} }$

Answer 2

Given ,

Initial velocity (u) = 200 m/s

Final velocity (v) = 0 m/s

Displacement (s) = 10 cm or 0.1 m

We know that ,

The Newton's third equation of motion is given by

$\boxed{ \sf{ {(v)}^{2} - {(u)}^{2} = 2as }}$

Thus ,

(0)² - (200)² = 2 × a × 0.1

-40000 = 2a/10

-400000 = 2a

a = -400000/2

a = -200000 m/s²

∴The retardation is -200000 m/s²