A boy stands on the edge of a cliff of height 60m. He throws a stone vertically upwards so that its distance, h, above the cliff top is given by h = 20t - 5t^2Calculate the time which elapses before the stone hits the beach.

The given function is:
h(t) = 20t-5t^2
where h(t) represents the height of the stone above the cliff.
Since the cliff is 60m above the sea, when the stone hits the beach, the value of h(t) is -60. Plugging this value, the function becomes:
-60 = 20t-5t^2
Take note that to solve quadratic equation, one side should be zero.
5t^2-20t-60=0
The three terms have a GCF of 5. Factoring out 5, the equation becomes:
5(t^2-4t-12) = 0
Dividing both sides by 5, it simplifies to:
t^2-4t-12=0
Then, factor the expression at the left side of the equation.
(t - 6)(t+ 2) = 0
Set each factor equal to zero. And isolate the t.
t-6 = 0
t=6
 
t+2=0
t=-2
Since t represents the time, consider only the positive value. (Let's assume that the time t is in seconds.) So the value of t when h(t)=-60 is:
t = 6
 
Therefore, the stone hits the beach 6 seconds after it was thrown.