Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem.
s = –16t2 + v0t + s0
You drop a coin from the top of a building. The building has a height of 996 feet.
s=-16t^2+996
s= ft
t= sec
Is there a question?
Your equation is correct.
To find the time it takes for the coin to hit the ground, we need to set the height, s, equal to zero and solve for t.
We are given that the initial height, s0, is 996 feet. Plugging this value into the equation, we have:
0 = -16t^2 + 996
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = -16, b = 0, and c = 996. Plugging in these values, we get:
t = (0 ± √(0^2 - 4(-16)(996))) / (2(-16))
Simplifying further:
t = (± √(0 + 63,360)) / (-32)
t = (± 252) / (-32)
We can ignore the negative solution, as time cannot be negative in this context. Therefore, the positive solution gives us the time it takes for the coin to hit the ground:
t = 252 / 32
t ≈ 7.875 seconds
Therefore, it takes approximately 7.875 seconds for the coin to hit the ground when dropped from the top of the building.