What is the momentum

Question

During an ice show a 60.0 kg skater leaps into the air and is caught by an initially stationary 55.0 kg skater.

(a)

What is their final velocity in meters per second assuming negligible friction and that the 60.0 kg skater's original horizontal velocity was 4.00 m/s? (Enter a number.)

 m/s

(b)

How much kinetic energy is lost in joules? (Enter a number.)

 J

Answer 1

Assuming that there was negligible vertical movement,

a) Initial momentum= mass × velocity = 60Kg × 4m/s = 240Kgm/s

Assuming that the final velocity of both skater is = V m/s

Final momentum = ( 60 + 55)Kg × V m/s = 115V Kgm/s

Conservation of momentum says,

Initial total momentum = Final Total momentum

115V Kgm/s + 0 Kgm/s = 60 × V Kgm/s + 55 × V Kgm/s

=> V = 240/115 = 2.087

Final velocity 2.087 m/s

b)

Initial Kinetic energy= 1/2 × mass × velocity² = 0.5 × 60Kg × (4m/s)² = 480J

Final Kinetic energy = 0.5 × 115Kg × (240/115 m/s)² = 250.43J

Kinetic energy loss = Initial Kinetic energy - Final Kinetic energy

= 480J - 250.43J

= 229.57J

Kinetic energy loss is 229.57J