Question

A golf ball, thrown upwards, rises at a speed of v metres per second.

The ball reaches a maximum height of h metres.
h is proportional to the square of v.
When v = 10, h = 8
Work out the maximum height reached by the golf ball when v = 45

Answer 1

162 metres

Explanation:

Since h is proportional to the square of v, we know that their ratio must be constant, so
`v_1^2/h_1 = v_2^2/h_2` where v1 and v2 are velocities and h1 and h2 are their respective heights.

Since we are given that v = 10 and h = 8, we can set v1 = 10 and h1 = 8 and since we are trying to find the height for v = 45, we can set v2 = 45. Inputting these values into the equation and solving, we get

10^2/8 = 45^2/h2

h2 = 45^2/(10^2/8) = 162 metres

I hope this helps!