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?
1 second after the ball is thrown
2 seconds after the ball is thrown
3 seconds after the ball is thrown
4 seconds after the ball is thrown

Explanation:

Step1: Set height to 0

When the ball reaches the ground, \( h = 0 \). So we set the equation \( -16t^2 + 64t = 0 \).

Step2: Factor the equation

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

Step3: Solve for t

Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).

• For \( -16t=0 \), we get \( t = 0 \). This is the time when the ball is kicked from the ground.
• For \( t - 4=0 \), we get \( t = 4 \). This is the time when the ball reaches the ground again.

Answer:

4 seconds after the ball is thrown