A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) The maximum height to which it rises. (ii) The total time it takes to return to the surface of the earth.

Given Initial velocity of ball, u=49m/s
Let the maximum height reached and time taken to reach that height be H and t respectively.
Assumption: g=9.8 m/s² holds true (maximum height reached is small compared to the radius of the earth)
Velocity of the ball at maximum height is zero, v=0
Using the third equation of motion we get, v²−u²=2aH
0−(49)²=2×(−9.8)×H
⇒H=122.5 m
Using the first equation of motion we get, v=u+at
0=49−9.8t
⇒t=5s
∴Total time taken by ball to return to the surface, T=2t=10 s.