Question

A 1 kg wooden block hanging from a 1 meter rope is struck by a 10g bullet moving horizontally is observed to rise 5cm. Assuming the bullet is lodged within the block, what must have been the speed of the bullet initially?

Answer 1

Question#19424

A 1 kg wooden block hanging from a 1 meter rope is struck by a 10g bullet moving horizontally is observed to rise 5cm. Assuming the bullet is lodged within the block, what must have been the speed of the bullet initially?

Solution:

Let:

$$m _ {1} = 1 \, \text{kg}$$ $$m _ {2} = 10 \, g = 0.01 \, \text{kg}$$ $$H = 5 \, \text{cm} = 0.05 \, \text{m}$$

v-?

The kinetic energy of a bullet was transformed to the sum of potential energy the block and the bullet.

$$E k _ {\text{bullet}} = E p _ {\text{bullet}} + E p _ {\text{block}}$$ $$\frac{1}{2} m _ {2} v ^ {2} = m _ {2} g H + m _ {1} g H, \, g = 9.8 \, \text{m/s}^2$$ $$v = \sqrt {\frac {2 g H (m _ {2} + m _ {1})}{m _ {2}}}$$ $$v = \sqrt {\frac {2 * 9.8 * 0.05 (0.01 + 1)}{0.01}} = 9.95 \, \text{m/s}$$

Answer: 9.95 m/s.