Question

a soccer ball is punted with an initial upward velocity of 64 feet per second. in how many seconds will it reach the ground? use a graph to help you solve.

Explanation:

Step1: Identify the motion - equation

The height - time equation for vertical motion under gravity is $h(t)=-16t^{2}+v_{0}t + h_{0}$, where $v_{0}$ is the initial velocity and $h_{0}$ is the initial height. Assuming the ball is punted from the ground level, $h_{0} = 0$, and $v_{0}=64$ feet per second. So, $h(t)=-16t^{2}+64t$.

Step2: Set $h(t)$ equal to 0

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

Step3: Factor out the common factor

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

Step4: Solve for $t$

Using the zero - product property, if $ab = 0$, then either $a = 0$ or $b = 0$. So, $-16t=0$ gives $t = 0$ (corresponds to the initial time when the ball is punted) and $t−4=0$ gives $t = 4$.

Answer:

4