Question

A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2).
What is a reasonable time for it to take the baseball to land on the ground?

A 5 seconds

B 7 seconds

C 9 seconds

D 2 seconds

Answer 1

The function is $h(t) = -16t^2 + 80t + 224$, and according to the description of the function in the problem statement, we have the following:

at t=0 after being thrown (that is, at initial time), the height of the ball is calculated by h(0) as follows:

$h(0) = -16(0)^2 + 80(0) + 224=0+0+224=224$ (ft), which is the initial height, as expected.


At t=1 (sec), the height would be  $h(1) = -16(1)^2 + 80(1) + 224=-16+80+224=288$. 

etc.


The path is parabolic, as we know by seeing that the function is a quadratic polynomial function. This function has been given in factored form as well. From that we can see that the zeros of the function are t=7 and t=-2.

This means that at t=7 sec, the height h is 0, which means that the ball has hit the ground. t=-2 has no significance in the context of our problem so we just neglect it.


Answer: B) 7 sec

Answer 2

Answer:

7 seconds is fully correct, done the test.

Step-by-step explanation: