Question

15. USE A MODEL The height h(t) in feet of an object t seconds after it is propelled up from the ground with an initial velocity of 60 feet per second is modeled by the equation h(t) = -16t² + 60t. When will the object be at a height of 56 feet?​

Answer 1

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.