How do you find how much a ball rises on a moving object

A science student riding on a flatcar of a train moving at a constant speed of 5.8 m/s throws a ball toward the caboose along a path that the student judges as making an initial angle of 53° to the horizontal. The teacher, who is standing on the ground nearby, observes the ball rising vertically. How high does the ball rise?

Horizontal component of ball velocity is same as train, = 5.8m/sec.
Initial vertical component = (tan 53) x 5.8, = 7.69m/sec.
Height observed to rise = (v^2/2g) = 3 metres above release.