Both Rachel and Dominique throw tennis balls into the air. At any time, t, the height, h, of Rachel’s 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, h = -16t2 + 30t - 5, but with an initial velocity, v, double that of Rachel’s. Which equation best models the height of Dominique’s tennis ball?

Dominique throws his tennis ball with the same acceleration, a, from the same initial height, h = -16t2 + 30t - 5, but with an initial velocity, v, double that of Rachel’s.

We have to find:

Which equation best models the height of Dominique’s tennis ball?

Solution:

The equation we have been given is:

h = –16t2 + 30t + 5.

where -16 is the acceleration

30 is the initial velocity

5 is the initial height

So when the initial velocity is doubled then the final equation we get is:

h = -16t^2+60t+5

Thus the equation that models the height of Dominique's tennis ball is

h = -16t^2+60t+5

erinna erinna · Answer 2 · 2019-10-06T08:14:42+02:00

Answer:

[tex]h=-16t^2+60t+5[/tex]

Step-by-step explanation:

The general equation of projectile motion is

[tex]y=\frac{1}{2}at^2+vt+h_0[/tex] ....(1)

where, a is acceleration, v is initial velocity and [tex]h_0=5[/tex].

It is given that Rachel’s ball is modeled by the equation

[tex]y=-16t^2+30t+5[/tex] .... (2)

On comparing both sides we get

[tex]\frac{1}{2}a=-16[/tex]

[tex]v=30[/tex]

[tex]h_0=5[/tex]

It is given that Dominique throws his tennis ball with the same acceleration, a, from the same initial height but with an initial velocity, v, double that of Rachel’s.

For Dominique's model

[tex]\frac{1}{2}a=-16[/tex]

[tex]v=2\times 30=60[/tex]

[tex]h_0=5[/tex]

Therefore, Dominique’s ball is modeled by the equation [tex]h=-16t^2+60t+5[/tex].