Question

Sloane kicked a soccer ball at a speed of 56 feet per second. If the ball never leaves the ground, then it can be represented by the function H(t) = −16t2 + 56t. Determine the time the ball traveled. T = 56 seconds t = 16 seconds t = 3.5 seconds t = 0.29 seconds

Answer 1

Third option:
`t=3.5\ seconds`

Explanation:

Given the function:

`H(t)=-16t^2 +56t`

Since the ball never leaves the ground, you need to substitute
`H(t)= 0` in the function in order to determine the time the soccer ball traveled:

`0=-16t^2 +56t`

Factorizing, you get:

`0=-8t(2t-7)`

Then:

`0=-8t\\\\t=0\ seconds\\\\\\\\0=2t-7\\\\7=2t\\\\t=3.5\ seconds`

Therefore the time the ball traveled was:

`t=3.5\ seconds`