Question

Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

Answer 1

0.18 < t < 2.82.

Explanation:

When h = 8 feet:

-16t^2 + 48t = 8

-16t^2 + 48t - 8 = 0

-2t^2 + 6t - 1 = 0

2t^2 - 6t + 1 = 0

Solving we get t = 0.18 and 2.82 seconds. At these times the stick is 8 feet off the ground.

Our inequality is 0.18 < t < 2.82.

Answer 2

`0.178<t<2.823`

Explanation:

Given that Tim throws a stick straight up in the air from the ground.

The function

`h = -16t^2 + 48t`

models the height, h, in feet, of the stick above the ground after t seconds

When height is more than 8 feet we have

`h = -16t2 + 48t>8\\2t^2-6t+1>0\\`

Solution for this inequality would be

`0.178<t<2.823`