Answer to Question #188815 in Classical Mechanics for Robin

Question

A ball is thrown at time t = t0 vertically upwards with the speed u. The air resistance can be neglected.  

1. What is the average velocity of the ball, in size and direction, from time t0 until the ball reaches its highest point?
2. What is the mean velocity of the ball, in size and direction, from the time t0 until the ball returns to the height from which it was thrown?

Answer 1

$t_1=\frac ug,~ s=\frac{u^2}{2g},$

1)

$<u_1>=\frac{s}{\Delta t}=\frac{\frac{u^2}{2g}}{\frac ug -t_0}=\frac{u^2}{2(u-gt_0)},$

2)

$<u_2>=\frac{s-s}{2\Delta t}=0.$