If an object is dropped from a height of 144 ft, the function h(t) = –16t² + 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
I think it is 3s...?
Yes, because that will give you a value of 0 height in 3 s.
Thank you
Thank
To determine when the object will hit the ground, we need to find the value of t when the height is 0.
Given that the function is h(t) = -16t² + 144, we can set h(t) equal to 0 and solve for t:
-16t² + 144 = 0
To solve this quadratic equation, we can factor out a common factor of -16:
-16(t² - 9) = 0
Now we can set each factor equal to 0:
t² - 9 = 0
This equation can be factored as a difference of squares:
(t - 3)(t + 3) = 0
Setting each factor equal to 0:
t - 3 = 0 or t + 3 = 0
Solving for t:
t = 3 or t = -3
Since time cannot be negative in this context, we discard the solution t = -3.
Therefore, the object will hit the ground at t = 3 seconds.
So, your initial guess of 3s is correct.