Question

I need help with 38c

Answer 1

Let me try and help. I don't know the level of physics that this question assumes. Can you find the speed of the mass in the circular orbit. If so you know its present energy,momentum and angular momentum. The explosion is an internal force and does not change the momentum of the system ie the two pieces, but it does increase the energy of system. Also we know that the immediate direction of the larger mass has not changed because the small mass has zero velocity so the larger masses velocity direction is not changed due to conservation of momentum.
You want to find the farthest distance from the earth. So the path being an ellipse will have its farthest point on the major axis at a distance from the earth where the kinetic energy is the smallest. We also know that angular moment is conserved since the explosion produces not net external forces to change it. The distance from the earth of a orbiting body for an ellipical orbit depends on the total energy, the angular momentum , and the cosine of the angle between the distance vector and the major axis. For this case cosine of the angle is 1. Do you have this information available?

Answer 2

@gleem While concise, that worked out perfectly. Thanks. I kept having trouble logging on and it was lagging so I couldn't see your response at first.