An Arrow (0.5 kg) travels with velocity 20 m/s to the right when it pierces an apple (2 kg) which is initially at rest. After the collision, the arrow and the apple are stuck together. Assume that no external forces are present and therefore the momentum for the system is conserved. What is the final velocity (in m/s) of apple and arrow after the collision

4 m/s

Explanation:

From the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

mu+m'u' = V (m+m') ... Equation 1

Where m = mass of the arrow, u = initial velocity of the arrow, m' = mass of the apple, u' = initial velocity of the apple, V = Final velocity of the apple and the arrow after collision.

make V the subject of the equation

V = (mu+m'u') / (m+m') ... Equation 2

Given: m = 0.5 kg, m' = 2 kg, u = 20 m/s, u' = 0 m/s (initially at rest)

Substitute into equation 2

V = (0.5*20+2*0) / (2+0.5)

V = 10/2.5

V = 4 m/s.

Hence the final velocity of the apple and the arrow after the collision = 4 m/s