Question

a baseball is thrown into the air from the top of a 224-foot tall building. the baseballs approximate height over time can be represented by the quadratic equation (h(t) = -16t^2 + 80t + 224), where (t) represents the time in seconds that the baseball has been in the air and (h(t)) represents the baseballs 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?

2 seconds
7 seconds
5 seconds

Explanation:

Set the height to zero for landing

$$ h(t) = 0 \implies -16(t - 7)(t + 2) = 0 $$

Solve for the time variable

$$ t - 7 = 0 \implies t = 7 $$

$$ t + 2 = 0 \implies t = -2 $$

Determine the viable solution in context

$$ t \ge 0 \implies t = 7\text{ seconds} $$

Answer:

• 2 seconds
• 7 seconds (Correct answer)
• 5 seconds