Final answer:
To determine when the object reaches 56 feet in height, the given equation h(t) = -16t² + 60t is set to 56 and solved for t, yielding two possible times: 7/4 seconds and 2 seconds, after being propelled upwards.
Step-by-step explanation:
To find when the object will be at a height of 56 feet, we need to set the equation h(t) = -16t² + 60t equal to 56 and solve for t:
56 = -16t² + 60t
Moving all terms to one side, we get:
-16t² + 60t - 56 = 0
Divide by -4 to simplify:
4t² - 15t + 14 = 0
Factor the quadratic equation:
(4t - 7)(t - 2) = 0
Setting each factor equal to zero gives us the possible values for t:
4t - 7 = 0 or t - 2 = 0
t = 7/4 seconds or t = 2 seconds
Therefore, the object will be at a height of 56 feet at 7/4 seconds and again at 2 seconds after it is propelled up from the ground.