Question

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?

Answer 1

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

Explanation:

The general equation of projectile motion is

`y=(1)/(2)at^2+vt+h_0` ....(1)

where, a is acceleration, v is initial velocity and
`h_0=5`.

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

`y=-16t^2+30t+5` .... (2)

On comparing both sides we get

`(1)/(2)a=-16`

`v=30`

`h_0=5`

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

`(1)/(2)a=-16`

`v=2* 30=60`

`h_0=5`

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

Answer 2

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

Explanation:

We have given that:

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.

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