Question

A ball rolls down the side of a hill with a height of 48.18 calculate the height of the ball when it is at half its final velocity you may ignore air resistance and friction

Answer 1

The height reached at half of its final velocity is 12.05 m.

How to calculate the height of the ball at half velocity?

The final velocity of the ball is calculated by applying conservation of energy as follows;

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √2gh

v = √ (2 x 9.8 x 48.18)

v = 30.73 m/s

The half of the final velocity is calculated as;

u = 0.5 x 30.73 m/s

u = 15.365 m/s

The height reached at 15.365 m/s is calculated as follows;

2gh = u²

h = u²/2g

h = (15.365²) / ( 2 x 9.8)

h = 12.05 m