Question

Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 32feet above the ground, the function h(t)=−16t2+48t+32 models the height, h, of the ball above the ground as a function of time, t. At what time will the ball reach a height of 64feet?

Answer 1

Given:

The height from which the ball is thrown= 32 feet

Function of height as a function of temperature: h(t)= -16t^2 + 48t+32

To find:

Time at which the ball reaches a height of 64 feet.

Solution:

When the ball reaches 64 feet, it means that the ball travelled (64-32) feet as Gianna threw the ball from the top floor of her middle school which was 32 feet above the ground.

Now, putting the value of h in the equation of height, we get:

32 = -16t^2 + 48t + 32

-16t^2 + 48t = 0

t(-16t +48) = 0

t= 0 (not possible)

and -16t + 48 =0

16t = 48

t= 3 sec

Since t cannot be 0, therefore at t=3, the ball reach a height of 62 feet.