Answer:
The coin hits the ground approximately 0.94 seconds after it is dropped from the top of the building.
Explanation:
d = -16t^2 + vt + h
where t is the time elapsed in seconds, v is the initial velocity of the object in feet per second, and h is the initial height of the object in feet.
In this problem, the initial height of the coin is not given, but we can assume that it is dropped from rest, so its initial velocity is 0. Then the ecuation is:
d = -16t^2 + h
where h is the initial height of the coin.
We are given that the equation for the distance d of the coin is:
d = -161t^2 + 144
Comparing this equation with the general equation for the distance of a falling object, we can see that the initial height of the coin is h = 0 and the initial velocity is v = 0.
To find the time it takes for the coin to hit the ground, we need to solve the equation:
d = 0
-161t^2 + 144 = 0
Solving for t, we get:
t^2 = 144/161
t = √(144/161)
t ≈ 0.94 seconds
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