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 coefficients for Rachel's ball

For Rachel's ball, the height - time equation is $h=-16t^{2}+30t + 5$. Comparing with $h(t)=at^{2}+vt+h_{0}$, we have $a=-16$, $v = 30$, and $h_{0}=5$.

Step2: Determine coefficients for Dominique's ball

Dominique has the same acceleration and initial height as Rachel, so $a=-16$ and $h_{0}=5$. Dominique's initial velocity is double that of Rachel's. Rachel's initial velocity $v = 30$, so 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 $h(t)=at^{2}+vt+h_{0}$. We get $h=-16t^{2}+60t + 5$.

Answer:

$h=-16t^{2}+60t + 5$ (corresponding to the last option in the multiple - choice list)