First slide

Rectilinear Motion

Question

A bullet, incident normally on a wooden plank, loses one-tenth of its speed in passing through the plank. The least number of such planks required to stop the bullet is

Moderate

A

5
B

6
C

7
D

8

Solution

Let v be the speed of the bullet incident on the first plank. Its speed after it passes the plank $= \frac{9 v}{10}$ . If x is the thickness of the plank, the deceleration a due to the resistance of the plank is given by
$2 ax = v^{2} - {(\frac{9 v}{10})}^{2} = \frac{19 v^{2}}{100} (1)$
Suppose the bullet is stopped after passing through n such planks. Then the distance covered by the bullet is s = nx. Thus, we have
$v^{2} - 0 = 2 as = 2 anx$
$\begin{array}{l} or n = \frac{v^{2}}{2 ax} = \frac{v^{2} \times 100}{19 v^{2}} [use Eq. (i) above] \\ = \frac{100}{19} = 5 .26 \end{array}$
Thus the minimum number of planks required is 6. Hence the correct choice is (2).

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