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
Answer:
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
Step-by-step 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