Question

A soccer ball is kicked from the ground. After travelling a horizontal distance of 25m, it just passes over a 2m tall fence before hitting the ground at a horizontal distance of 35m.

a) Determine an equation to represent the height of the ball relative to its horizontal distance away from its starting point(origin).

b) What is the maximum height of the ball?

Answer 1

You know that y(0) = y(35) = 0

So, y = ax(x-35)
Since y(25) = 2,
a(25)(25-35) = 2
a = -1/125

y(x) = -1/125 x(x-35)

max height is achieved at x = 35/2, so
y(35/2) = 49/20 = 2.45