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
