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?

Answer 1

7 seconds

Explanation:

We assume h(t) represents the height above ground, so that h(t) = 0 will be the point where the ball hits the ground.

The factored form of the equation tells us ...

h(7) = -16(7 -7)(7 +2) = 0

So, the baseball will land on the ground when t=7, seven seconds after first being thrown into the air.

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The other value of t that makes h(t) = 0 is -2. Since we only count time after the ball is thrown, t=-2 is an extraneous solution.