Question

The function h defined by h(t)=(-4.9t + 29.4)(t+2) models the height in meters, of an object t seconds after it is launched. When will the object hit the ground?

Answer 1

The time the object will hit the ground is 2 s.

Explanation:

Given;

h(t) = (-4.9t + 29.4)(t + 2)

Open the bracket;

h(t) = -4.9t² + 29.4t -9.8t + 58.8

h(t) = -4.9t² + 19.6t + 58.8

When the object hit the ground, the final velocity will be zero;

`v = (dh)/(dt) = 0 \\\\(dh)/(dt) = -9.8t + 19.6 = 0\\\\9.8t = 19.6\\\\t = (19.6)/(9.8) \\\\t = 2 \ s`

Therefore, the time the object will hit the ground is 2 s.