Question

A ball is thrown into the air with an initial upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h (t) = -16t² + 48t + 4. After how many seconds will the ball hit the ground?

Answer 1

After how many seconds will the ball hit the ground?​

Finding the equation

Since h is the height in feet, when the ball touch the groun then,

h(t) = 0 ft

replacing it in the equation we have that

0 = -16t² + 48t + 4

0 = -16t² + 48t + 4

This is the equation when the ball is on the ground. In order to find after how many seconds it hits it, we need to solve the equation for t.

In order to solve it we want to factor:

-16t² + 48t + 4 = 0

↓

16t² - 48t - 4 = 0

Factoring the equation

In order to factor it we want to find two numbers that satisfy that: