Question

A ball is thrown in the air from a platform at time t = 0 seconds. The height, h(t), of the ball can be modeled as a function of time, t, by the equation h(t) = -16t + 40t + 20. Approximately how many seconds after being thrown will the ball hit the ground?

2.37 seconds


1.25 seconds


2.93 seconds


0.13 seconds

Answer 1

Option C is the correct answer.

Explanation:

The height, h(t), of the ball can be modeled as a function of time, t, by the equation h(t) = -16t² + 40t + 20

When the ball hits the ground, we have h(t) = 0

h(t) = -16t² + 40t + 20 = 0

`t=(-40\pm √(40^2-4* (-16)* 20))/(2* (-16))=(-40\pm √(2880))/(-32)\\\\t=(-40\pm 53.67)/(-32)\\\\\texttt{t = 2.93s or t = -0.43s}`

Negative time is not possible, so time = 2.93 seconds.

Option C is the correct answer.