Question

A droplet of water flew vertically from a hot spring geyser at an initial speed of 40 m/s. The approximate height (h), in metres, that the droplet will reach, in (t) seconds is modelled by h = -5t² + 40t.
How long before the droplet will reach the ground?
Determine the maximum height reached by the droplet of water.

Answer 1

1)
let h = 0

so -5t²+40t = 0
t(-5t+40) = 0
t = 0(refused) or t =8 sec

2)
Maximum height is the vertex of the function

calculate the x coordinate of the vertex = -b/2a = -40/-10 = 4 sec.
calculate the x coordinate of the vertex = f(-b/2a) = f(4) = -5(4)² + 40(4) = 80 m.

So max. Height is 80 meters