In a target shooting game, wooden blocks are thrown into the air and shot in flight. A block of 0.8kg has a speed of 10 m/s at the top of its trajectory when it is hit by a bullet from below at an angel 60° from horizontal. The mass of the bullet is 5.0 g and its speed is 550m/s when it hits the block. The bullet is embedded in the block. What is the velocity of the block immediately after impact?
To find the velocity of the block immediately after the impact, we need to apply the law of conservation of momentum. According to this law, the total momentum before the impact is equal to the total momentum after the impact.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the initial velocity of the bullet as v_bi, the final velocity of the bullet as v_bf, and the final velocity of the block as v_f.
The momentum of the bullet before the impact can be calculated as:
P_bi = (mass of the bullet) * (initial velocity of the bullet)
P_bi = (0.005 kg) * (550 m/s)
The momentum of the block before the impact is given by:
P_block = (mass of the block) * (velocity of the block)
P_block = (0.8 kg) * (10 m/s)
Since momentum is conserved, the total momentum before the impact is equal to the total momentum after the impact:
P_bi + P_block = P_bf + P_f
Since the bullet is embedded in the block, the final velocity of the bullet will be equal to the final velocity of the block. Therefore, v_bf = v_f.
Substituting the known values into the equation, we have:
(0.005 kg) * (550 m/s) + (0.8 kg) * (10 m/s) = (0.005 kg + 0.8 kg) * (v_f)
After calculating the left side of the equation, we can solve for v_f to find the final velocity of the block.