A penny is dropped from a high-rise building that is 350 feet high. After 8.4 seconds, the penny hits the ground. Which one of the following quadratic models describe the height of the penny above ground as a function of the time elapsed since the penny was dropped?

Question

Quizplus · Accepted Answer

The height of the penny can be modeled using the equation: 
h(t) = -16t^2 + vt + h0 
where h0 is the initial height, v is the initial velocity (which is 0 because the penny is dropped), and t is time. 
In this case, h0 = 350 feet and v = 0. 
So the equation becomes: 
h(t) = -16t^2 + 350 
To find when the penny hits the ground, we can set h(t) = 0 and solve for t: 
0 = -16t^2 + 350 
16t^2 = 350 
t^2 = 350/16 
t = sqrt(350/16) 
t ≈ 3.937 seconds 
But we're told that the penny hits the ground after 8.4 seconds, so the model needs to account for the entire time. We can use the fact that the penny hits the ground to find the height at that time: 
h(8.4) = -16(8.4)^2 + 350 
h(8.4) ≈ -100.64 feet 
So the final equation is: 
h(t) = -16t^2 + 350 for 0 ≤ t ≤ 8.4 
This matches option B.

A Penny Is Dropped from a High-Rise Building That Is