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Finding Average Velocity

A wooden bloc...

Question

A wooden block is dropped from a tower of height 200 m. Simultaneously a bullet is fired from the foot of the tower aiming the block with the velocity of $100 {m s}^{- 1}$ . Given that the masses of both the block and the bullet , each equal to 100 g and the bullet is embedded in the block, find the maximum potential energyof the system of the block and the bullet. ( $g = 10 {m s}^{- 2}$ ) (Neglect the time of impact).

150 J

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450 J

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300 J

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250 J

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Solution

The correct option is B 450 J
$M_{B l o c k} = 100 g M_{B u l l e t} = 100 g$

initial

$S_{1} + S_{2} = 200 M \frac{1}{2} g t^{2} + 100 t - \frac{1}{2} g t^{2} = 200 t = 2 s e c S_{1} = 20 M S_{2} = 180 M$

At point P V of system is

$A t p o i n t P V o f s y s t e m i s (200 g) V = (100 g) [20] (^j) + (100 g) (80^j) 200 g V^j = 60 (100 g)^j V = 30 m / s$

After the impact energy will remain conserved

$P E_{j} + K E_{j} = P E_{f} + K E_{f} \frac{200}{1000} \times 10 \times 180 + \frac{1}{2} \times \frac{200}{1000} \times 900 = P E_{f} 360 + 90 = P E_{f} P E_{f} = 450 J$

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