Question
if an object from a height of 144 ft, the function h(t)=-16t^2+144 gives the height of the object after t seconds. when will the object hit the ground?
1.5 s
3 s
6 s
9 s
1.5 s
3 s
6 s
9 s
Answers
GPT 3.5
To find when the object will hit the ground, we need to find the value of t when h(t) is equal to 0 (since the height at that time would be 0, indicating that the object has hit the ground).
Setting h(t) to 0:
0 = -16t^2 + 144
To solve this quadratic equation, we can first divide both sides by -16:
0 = t^2 - 9
Next, we can factor this equation as the difference of squares:
0 = (t - 3)(t + 3)
Setting each factor equal to 0 and solving for t:
t - 3 = 0 --> t = 3
t + 3 = 0 --> t = -3
Since time cannot be negative in this context, the object will hit the ground after 3 seconds.
Therefore, the answer is 3 s.
Setting h(t) to 0:
0 = -16t^2 + 144
To solve this quadratic equation, we can first divide both sides by -16:
0 = t^2 - 9
Next, we can factor this equation as the difference of squares:
0 = (t - 3)(t + 3)
Setting each factor equal to 0 and solving for t:
t - 3 = 0 --> t = 3
t + 3 = 0 --> t = -3
Since time cannot be negative in this context, the object will hit the ground after 3 seconds.
Therefore, the answer is 3 s.