Question

A stone is projected vertically so that its position above ground level after t seconds is given by

h(t) = 100t – 5t2 meters, t > 0.
Which one of the following is the maximum height the stone can reach?

Answer 1

Explanation:

The height of the vertically projected stone is represented by the function,

h(t) = 100t – 5t^2

The given function is a quadratic equation. If values of height attained attained by the stone is plotted against time, the shape of the graph will be a parabola whose vertex would correspond to the maximum height obtained by the stone.

Vertex of the parabola = -b/2a

From the given equation,

a = - 5

b = 100

Vertex = - 100/ - 2× 5 = 100/10

Vertex = 10

Therefore, the maximum height the stone can reach is 10 meters