Answer:
Step-by-step explanation:
A. The total momentum of the system before the collision is:
P_before = m1v1 + m2v2
P_before = (2.50 kg)(15.00 m/s) + (64.00 kg)(-1.50 m/s)
P_before = 37.50 kg·m/s - 96.00 kg·m/s
P_before = -58.50 kg·m/s
where m1 = 2.50 kg is the mass of the ball, v1 = 15.00 m/s is the velocity of the ball, m2 = 64.00 kg is the mass of the astronaut, and v2 = -1.50 m/s is the velocity of the astronaut (since they are moving in opposite directions).
B. In an inelastic collision, the objects stick together after colliding. The momentum after the collision is:
P_after = P_before = -58.50 kg·m/s
C. To find the velocity of the objects after the collision, we use the conservation of momentum and the fact that the objects stick together:
P_after = (m1 + m2)vf
where vf is the final velocity of the combined object. Solving for vf:
vf = P_after / (m1 + m2)
vf = (-58.50 kg·m/s) / (2.50 kg + 64.00 kg)
vf = -0.89 m/s (to two decimal places)
Therefore, the velocity of the objects after the collision is -0.89 m/s, which means they move in the direction of the astronaut's initial velocity.