Question

A basketball rolls to the right with a velocity of 4 meters per second. It is pushed up and accelerated up for 2 seconds with an acceleration of 4 meters per second . Then for 1 second it is pushed and accelerated down with an acceleration of 12 meters per second . What is its final velocity and in exactly what direction

Answer 1

NOTE - acceleration is in m/s^2 NOT m/s

Its horizontal velocity component does not change since there is no horizontal force
u = 4 m/s

Vertical
Vi = 0
v = Vi + a t
v = 0 + 4 * 2 = 8 m/s

v = 8 - 12 (1) = -4 m/s
so in the end
u = 4 and v = -4

speed = 4 sqrt 2
direction = 45 degrees down from horizontal