An archer shoots an arrow toward a 300 g target that is sliding in her direction at a speed of 2.45 m/s on a smooth, slippery surface. The 22.5 g arrow is shot with a speed of 40.5 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?
8.3
To find the speed of the arrow after passing through the target, we can use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision can be calculated by multiplying the mass of the arrow by its initial velocity:
Initial momentum of the arrow = (mass of arrow) * (initial velocity of arrow)
= 0.0225 kg * 40.5 m/s
The momentum after the collision can be calculated by multiplying the mass of the arrow by its final velocity:
Final momentum of the arrow = (mass of arrow) * (final velocity of arrow)
Since the target is stopped by the impact of the arrow, its final velocity is 0 m/s. Therefore, the momentum after the collision is:
Final momentum of the arrow = 0.0225 kg * 0 m/s
= 0
Since the total momentum before the collision is equal to the total momentum after the collision, we can equate the two values:
Initial momentum of the arrow = Final momentum of the arrow
0.0225 kg * 40.5 m/s = 0
From this equation, we can see that the initial momentum of the arrow is equal to 0, which means that the speed of the arrow after passing through the target is also 0 m/s.