both rachel and dominique throw tennis balls into the air. at any time, t, the height, h, of rachels ball is…

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?\nh(t) = at² + vt + h₀\n○ h = -16t² + 30t + 10\n○ h = -32t² + 60t + 10\n○ h = -32t² + 30t + 5\n○ h = -16t² + 60t + 5

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?\nh(t) = at² + vt + h₀\n○ h = -16t² + 30t + 10\n○ h = -32t² + 60t + 10\n○ h = -32t² + 30t + 5\n○ h = -16t² + 60t + 5

Answer

Answer:

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

Explanation:

Step1: Identify coefficients for Rachel's ball

For Rachel's ball, $h=-16t^{2}+30t + 5$, so $a=-16$, $v = 30$, $h_0=5$.

Step2: Determine coefficients for Dominique's ball

Dominique has same $a=-16$ and $h_0 = 5$, and $v$ is double of Rachel's, so $v = 2\times30=60$.

Step3: Write the equation

Substitute $a=-16$, $v = 60$, $h_0=5$ into $h(t)=at^{2}+vt+h_0$, we get $h=-16t^{2}+60t + 5$.