First slide

The 3 equation for uniform acc

Question

A bullet fired into a wooden block loses 75% of its velocity after penetrating 15 cm into it' How much further distance it has to penetrate to be stopped completely ?

Moderate

A

1 cm
B

2 cm
C

3 cm
D

4 cm

Solution

Let u be the initial velocity of the bullet and a be the retardation of the wooden board assumed to be constant. Using the formula v² =u² +2as, we have
$\begin{array}{l} {(\frac{u}{4})}^{2} = u^{2} - 2 a \times 15 \\ or \frac{u^{2} - 16 u^{2}}{16} = - 30 a \end{array}$
$∴ u^{2} = 32 a . . . (1)$
Let it travel a further distance s before it is stopped. Then
$0 = {(\frac{u}{4})}^{2} - 2 as$
or u² = 32 as … (2)
From eqs. (1) and (2).
32 a s = 32 a or s = 1 cm

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