Question

The function f(t)=^ - 16t^ 2 +84t models the height of a ballt seconds after it was kicked straight up into the air. How many seconds does it take the ball to hit the ground ?

Answer 1

5.25 seconds

Explanation:

When the ball hits the ground the height is zero

Equate f(t) to zero and solve for t , that is

- 16t² + 84t = 0 ← factor out - 4t from each term

- 4t(4t - 21) = 0

Equate each factor to zero and solve for t

- 4t = 0 ⇒ t = 0

4t - 21 = 0 ⇒ 4t = 21 ⇒ t =
`(21)/(4)` = 5.25

t = 0 is the time when the ball is kicked

t = 5.25 is the time taken for the ball to hit the ground