Calculate the ball speed when it fall back to his hand and determine the time of the ball in the air before it fall back to the hand of the student.

Question

A student throws a ball vertically upwards with a velocity of 30 m/s. Given

earth gravity, g = 10 N/kg.

Answer 1

The speed (v) of an object after some acceleration (a) for a time (t) is given by the equation :

v_final = v_initial + a*t

After the ball is thrown upwards, gravity will accelerate it, albeit negatively (because pulls back down) so it slows to 0 upwards speed. After that brief instant, gravity will continue to accelerate it downwards and mirror the first half of the motion. This means that the ball will return to the students hand at the same speed at which it left (in this case 30 m/s) and the total time will be twice the time that it took to reach that brief 0 speed instant.

Therefore using the equation above where v_final = 0 m/s , v_initial = 30 m/s , a = g = -10 N/kg = -10 m/s² :

0 m/s = 30 m/s + (-10 m/s²)*t , solving for t , t = (-30 m/s) / (-10 m/s²) = 3 seconds. Double for the total time of 6 seconds.