0-kilogram child moving at 4.0 meters per second jumps onto a 50-kilogram sled that is initially at rest on a long, frictionless, horizontal sheet of ice. [INF] a. Determine the speed of the child-sled system after the child jumps onto the sled. b. After coasting at constant speed for a short time, the child jumps off the sled in such a way that she is at rest with respect to the ice. Determine the speed of the sled after the child jumps off

This question is incomplete, the complete question is;

A 30-kilogram child moving at 4.0 meters per second jumps onto a 50-kilogram sled that is initially at rest on a long, frictionless, horizontal sheet of ice.

a. Determine the speed of the child-sled system after the child jumps onto the sled.

b. After coasting at constant speed for a short time, the child jumps off the sled in such a way that she is at rest with respect to the ice. Determine the speed of the sled after the child jumps off

a) the speed of the child-sled system after the child jumps onto the sled is 1.5 m/s

b) the speed of the sled after the child jumps off is 2.4 m/s

Explanation:

Given that;

Weight of the child m_c = 30 kg

u = 4 m/s

M = 50 kg

a) the speed of the child-sled system after the child jumps onto the sled.

Using conservation of momentum;

P_i = P_f

30 × 4 = 50(v) + 30(v)

120 = 80(v)

v = 120 / 80

v = 1.5 m/s

therefore, the speed of the child-sled system after the child jumps onto the sled is 1.5 m/s

b) the speed of the sled after the child jumps off .

Also using conservation of momentum;

mv1 = mv2

(30+50) × 1.5 = (30 × 0) + (50 × v2 )

80 × 1.5 = 50v2

v2 = 120 / 50

v2 = 2.4 m/s

Therefore the speed of the sled after the child jumps off is 2.4 m/s