If an object is dropped from a height of 144 ft, the function gives the height of the object after t seconds. When will the object hit the ground? (1 point) Responses 1.5 s 1.5 s 3 s 3 s 6 s 6 s 9 s
The height of the object after t seconds can be calculated using the formula h(t) = -16t^2 + 144, where h(t) is the height in feet.
We want to find when the height of the object is 0, which means it has hit the ground. So we set h(t) = 0 and solve for t:
-16t^2 + 144 = 0
Dividing both sides by -16 gives:
t^2 - 9 = 0
Factoring the equation, we have:
(t + 3)(t - 3) = 0
Setting each factor equal to zero:
t + 3 = 0 or t - 3 = 0
Solving for t, we have:
t = -3 or t = 3
Since time cannot be negative, the object hits the ground after 3 seconds.