A50 kg archer, standing on frictionless ice, shoots a 100 g arrow at speed 100 m/s. what is the recoil speed of the archer?

The recoil speed of the archer is -0.2 m/s

Explanation:

To calculate the recoil speed of the archer, we use the equation of law of conservation of momentum, which is:

where,  

= mass of archer = 50 kg

= Initial velocity of archer = 0 m/s

= Final velocity (recoil speed) of archer = ? m/s

= mass of arrow = 100 g = 0.100 kg   (Conversion factor:  1 kg = 1000 g)

= Initial velocity of arrow = 0 m/s

= Final velocity of arrow = 100 m/s

Putting values in above equation, we get:

Hence, the recoil speed of the archer is -0.2 m/s