Question

Lugi is trying to hit a turtle shell. The height of

Lugi's feet above the ground is given by the
functionh(t) = -16t² +961 + 2.
How long does it take for Lugi to hit the shell on the ground?
A. 3 seconds
B. 146 seconds
0.6.02 seconds
D. 16 seconds

Answer 1

C. 6.02sec

Explanation:

Given

`h(t) = -16t\² +96t + 2`

Required

Time to hit the ground

When the turtle shell hits the ground,
`h(t) = 0`

So:

`0 = -16t\² +96t + 2.`

Solving using quadratic formula:

`t = (-b\±√(b^2-fac))/(2a)`

Where:

`a = -16; b =96; c = 2`

So:

`t = (-96\±√(96^2-4 * -16 * 2))/(2*-16)`

`t = (-96\±√(9344))/(-32)`

`t = (-96\±96.66)/(-32)`

Split:

`t = (-96+96.66)/(-32)` or
`t = (-96-96.66)/(-32)`

`t = (0.66)/(-32)` or
`t = (-192.66)/(-32)`

`t = -0.020625` or
`t = 6.020625`

So time can't be negative, we have:

`t = 6.020625`

Option C answers the question