From a platform an object is projected vertically into air. Its height, h metres above ground level after t seconds is modelled by equation h=3+20t-5t^2.

Question

At what height above the ground is the platform from which the object was projected?
Calculate the time when the object will again be at the same height as the platform
At what time, correct to 2 decimal places does the object reach the ground?

Answer 1

a) at that time, t = 0, so
h = 3 + 0 + 0 = 3 m
b) you want the t, when h = 3
3 = 3 + 20t - 5t^2
5t^2 - 20t = 0
t(5t - 20) = 0
t = 0 or t = 4

c) when it hits the ground, h = 0
5t^2 - 20t - 3 = 0

solve, using your favourite method of solving quadratics, reject the negative answer.