Answer to Question #96928 in Mechanics | Relativity for Dude

Question

Ball landed on the ground with impact velocity of 30 m/s.

a.) from how high it was dropped?
b.) where was it at time= 0.5s?
c.) how long did it take to fall?

Answer 1

The final velocity of the ball is $v_f=30\:\rm m/s,$ the acceleration due gravity $g=9.8\:\rm m/s^2.$

(a) Height

$$H=\frac{v_f^2}{2g}=\frac{30^2}{2\times 9.8}=46\:\rm m$$

(b) Position at 0.5s

$$y=H-\frac{gt^2}{2}=46-\frac{9.8\times 0.5^2}{2}=44.8\:\rm m\quad (above \; the \; ground)$$

(c) Time of motion

$$t=\frac{v_f}{g}=\frac{30}{9.8}=3\:\rm s$$