Question

This equation is a mathematical model for the motion of the ball. A model is a representation of a phenomenon or object. You can use this mathematical model to predict the location of the ball if you know the time, or the time when the ball will reach a certain position. Let's use this model to predict the time for the ball to reach the flag. You can do this by setting the position equal to the position of the flag in your trial. Then, use algebra to solve for t, the time when the ball is at that location. Show your work in the space below.

Answer 1

`P(t) = 50t +25`

`t = 2.5s`

Step-by-step explanation:

Given

See attachment for graph

Solving (a): The graph equation.

Pick two points on the line of the graph

`(t_1,P_1) = (0.9,70)`

`(t_2,P_2) = (0.7,60)`

Calculate the slope (m)

`m = (P_2 - P_1)/(t_2 - t_1)`

`m = (60 - 70)/(0.7 - 0.9)`

`m = (-10)/(-0.2)`

`m = 50`

The equation is then calculated using:

`P(t) = m(t - t_1) + P_1`

`P(t) = 50(t - 0.9) + 70`

`P(t) = 50t - 45+ 70`

`P(t) = 50t +25`

Solving (b): Solve for t when
`P(t) =150cm`

We have:

`P(t) = 50t +25`

Substitute:
`P(t) =150cm`

`150 = 50t + 25`

Collect like terms

`50t = 150 - 25`

`50t =125`

Divide both sides by 50

`t = (125)/(50)`

`t = 2.5s`