Question

sharon kicks a ball from the ground into the air with an upward velocity of 64 feet per second. the function $h=-16t^{2}+64t$ models the height $h$, in feet, of the ball at time $t$, in seconds. when will the ball reach the ground again? 4 seconds after the ball is thrown 1 second after the ball is thrown 3 seconds after the ball is thrown 2 seconds after the ball is thrown

Explanation:

Step1: Set height h to 0

When the ball reaches the ground, $h = 0$. So we set the equation $-16t^{2}+64t = 0$.

Step2: Factor out common term

Factor out $-16t$ from the left - hand side of the equation: $-16t(t - 4)=0$.

Step3: Use zero - product property

If $ab = 0$, then either $a = 0$ or $b = 0$. So we have $-16t=0$ or $t - 4=0$.
The solution of $-16t=0$ is $t = 0$ (this is the time when the ball is initially kicked).
The solution of $t - 4=0$ is $t = 4$.

Answer:

4 seconds after the ball is thrown