Question

the height that a ball bounces varies directly as the height from which it is dropped. A ball dropped from a height of 20cm bounces 16cm

a) Find the height of the bounce if the ball is dropped from a height of 280cm

b) Find from waht height the ball was dropped if it bounces to a height of 120cm

Thanks in advance.

Answer 1

let h be the new height, let x be the height it was dropped from, then

h = kx, where k is a constant
when x=20, h=16
so 16=k20
k = 16/20 = 4/5
then h =4x/5

a)when x= 280
h = 4(280)/5 = 224

b) when h = 120
120 = 4x/5
600 = 4x
x = 150