Question

both rachel and dominique throw tennis balls into the air. at any time, t, the height, h, of rachels ball is modeled by the equation h = -16t² + 30t + 5. dominique throws his tennis ball with the same acceleration, a, from the same initial height, h₀, but with an initial velocity, v, double that of rachels. which equation best models the height of dominiques tennis ball? h(t)=at² + vt+h₀ o h = -16t² + 30t + 10 o h = -32t² + 60t + 10 o h = -32t² + 30t + 5 o h = -16t² + 60t + 5

Explanation:

Step1: Identify the general height - time formula

The general formula for the height of an object in vertical - motion under the influence of gravity is $h(t)=at^{2}+vt + h_{0}$, where $a$ is the acceleration, $v$ is the initial velocity, and $h_{0}$ is the initial height. For Rachel's ball, $h=-16t^{2}+30t + 5$, so the acceleration $a=-16$, the initial velocity $v = 30$, and the initial height $h_{0}=5$.

Step2: Determine the values for Dominique's ball

Dominique has the same acceleration $a=-16$ and the same initial height $h_{0}=5$ as Rachel. But the initial velocity of Dominique's ball is double that of Rachel's. Since Rachel's initial velocity $v = 30$, Dominique's initial velocity $v_{D}=2\times30 = 60$.

Step3: Write the equation for Dominique's ball

Substitute $a=-16$, $v = 60$, and $h_{0}=5$ into the general formula $h(t)=at^{2}+vt + h_{0}$. We get $h=-16t^{2}+60t + 5$.

Answer:

$h=-16t^{2}+60t + 5$