An Arrow (0.2 kg) travels with velocity 50 m/s to the right when it pierces an apple (2.5 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

3.75 m/s

Explanation:

The arrow has a mass, M, of 0.2 kg and it travels with initial velocity, U, 50 m/s to the right. The apple of mass, m, 2.5 kg is initially at rest (u = 0 m/s).

After the collision, the arrow and the apple are stuck together. They have the same final velocity, V.

We are told to assume that no external forces are present and therefore the momentum for the system is conserved.

Using the Principle of conservation of momentum, we have that in a system of bodies:

Total initial momentum = Total final momentum

The total initial momentum is:

M*U + m*u = (0.2*50) + (2.5*0) = 10 kgm/s

The total final momentum is:

M*V + m*V = (M + m) * V = (0.2 + 2.5) * V = 2.67V kgm/s

Therefore:

10 = 2.67V

=> V = 10 / 2.67 = 3.75 m/s

The final velocity of the apple and arrow is 3.75 m/s.