A ball is thrown vertically upward from the ground. Its distance in feet from the ground in t seconds is s equals negative 16 t squared plus 240 t. After how many seconds will the ball be 864 feet from the ground?

t₁ = 3 s

Explanation:

In this exercise, the vertical displacement equation is not given

y = 240 t + 16 t²

Where y is the displacement, 240 is the initial velocity and 16 is half the value of the acceleration

Let's replace

864 = 240 t + 16 t²

Let's solve the second degree equation

16 t² + 240 t - 864 = 0

Let's divide by 16

t² + 15 t - 54 = 0

The solution of this equation is

t = [-15 ± √ (15 2 - 4 1 (-54)) ] / 2 1

t = [-15 ±√ (225 + 216) ] / 2

t = [-15 + - 21] / 2

We have two solutions.

t₁ = [-15 + 21] / 2

t₁ = 3 s

t₂ = - 18 s

Since time cannot have negative values, the correct t₁ = 3s