Ballistic Pendulum Problem

Question

My teacher doesn't teach us how to do our homework before we do it so I rely on KhanAcademy for the most part but this one's a bit tough.

A dart with mass md is launched toward a block of mass mb that is suspended from a string of length L. The dart is moving horizontally with speed v immediately before it strikes the block and remains embedded. The dart-block system then swings up to a point at which its center of mass reaches a maximum height H above its starting position, as shown at right above. The block’s mass mb is greater than the dart’s mass md.

Which of these underlined statements are correct vs incorrect and why:

Student 1: The speed of the system at height H is zero. Since it is moving in circular motion and centripetal acceleration is given by ac=v2r, the acceleration must also be zero.

Student 2: The acceleration of the system at height H can’t be zero, or the system would not swing back down. The acceleration must be equal to g at height H.

I'm pretty sure student one is mostly correct but I'm having some trouble explaining why (or if I'm even correct)

Answer 1

- The speed of the system at height H is 0 by definition of maximal height.

If it had a positive speed moving up, then at height H the system had not yet reached the maximum height.

If it had a positive speed moving down, then at height H the system had already passed a higher height.

- The system is subject to two forces -- gravity and the centripetal force due to tension in the string.

At height H, the centripetal force is 0 because the speed is 0.

So the system has only the gravitational acceleration g.

Student 1 would be right in all his statements, if the word "acceleration" were replaced by "centripetal acceleration".

Student 2 is right in all his statements.