A Crossbow and a Bolt: Conservation of Momentum

Calculation of the Recoil Velocity

A crossbow (5.0 kg) loaded with a bolt (0.10 kg) launches the bolt to the right with a speed of 25 m/s. To determine the velocity of the crossbow as it recoils, we can utilize the principle of conservation of momentum.

Conservation of Momentum

Momentum is the product of an object's mass and its velocity. In a closed system with no external forces, the total momentum remains constant before and after an event.

Initial Momentum

Before the crossbow is triggered, the system's total momentum is zero since the crossbow is stationary. Thus, the initial momentum of the system is 0 kg m/s.

Final Momentum

After launching the bolt (0.10 kg) with a speed of 25 m/s, the momentum of the bolt is (0.10 kg * 25 m/s = 2.5 kg m/s).

Applying Conservation of Momentum

In order for the total momentum of the system to remain constant, the crossbow must recoil in the opposite direction with a momentum equal in magnitude but opposite in direction to the momentum of the bolt.

Calculating the Recoil Velocity

The recoil velocity of the crossbow can be calculated as follows:

(mass of crossbow * velocity of crossbow) = (mass of bolt * velocity of bolt)

(5.0 kg * velocity of crossbow) = (0.10 kg * 25 m/s)

velocity of crossbow = (0.10 kg * 25 m/s) / 5.0 kg

velocity of crossbow = 5 m/s

Therefore, the velocity of the crossbow as it recoils after launching the bolt to the right with a speed of 25 m/s is 5 m/s.