Question

a ball is dropped from the height of 64 feet. its height can be modeled by the function h(t)=-16t^2+64, where t is the time in seconds since it's dropped. find how long it takes the ball to fall 36 feet (hint: first find its height) PLSSS HELP!!!

Answer 1

Answer:

It takes 1.323 seconds for the ball to fall by 36 feet

Step-by-step explanation:

The height of the ball dropped from a height of 64 ft is modeled by the equation:

h(t) = -16t² + 64 where t is the time in seconds.

To find the time it takes to fall 36 ft, we substitute h(t) too be 36 ft and then solve the resulting quadratic function.

Substituting h(t) to be 36 ft:

36 = -16t² + 64

multiply through by -1

-36 = 16t² - 64

add 36 to both sides

16t² -64 + 36 = -36 + 36

16t² - 28 = 0

add 28 to both sides

16t² - 28 + 28 = 0 +28

16t² = 28

Divide both sides by 28

16t²/16 = 28/16

t² = 1.75

Find squre root of both sides

√t² = √1.75

t = 1.323 seconds

It takes 1.323 seconds for the ball to fall by 36 feet