How Do You Calculate the Trajectory of a Tennis Ball in Physics?

[basedgod]

Hi, I'm a 1st year undergrad but I left school 7 years ago! Really struggling with the physics of my course. I have some coursework to hand in for Monday but I'm a little bit stuck. I have gone over my notes and have been browsing the internet for the past hour but I don't know what to do.
The question comes in four parts. The latter parts are very simple to do using equations I have found on wikipedia, but Question A specifically asks "Determine the trajectory equation of the ball after being hit (give all the details from where the equation comes from)"

This is an 8 mark question so it seems to be quite in depth.

More background to the original problem;

A tennis player1 located on the line at the back of the court attempts to “lobe” his competitor. The tennis player2 stands 2 meters behind the net facing player1 who hits the ball in 0 (origin), 9 meters away from the net and at a height of h=0.5m above the ground. The tennis ball travels with a speed Vo=12 m/s, with the velocity vector at an angle = 60o with the ground.
g = 9.81 m/s2.


As I said, the rest of the coursework(questions B, C, D) are relatively simple and just asks you to solve some problems, which I can do using the equations I have found online.

However part A is really bothering me. I'm not sure how to go about constructing an equation and how to give details of how I arrived at it.

Any help would be much appreciated.

 

[berkeman]

Hi, I'm a 1st year undergrad but I left school 7 years ago! Really struggling with the physics of my course. I have some coursework to hand in for Monday but I'm a little bit stuck. I have gone over my notes and have been browsing the internet for the past hour but I don't know what to do.
The question comes in four parts. The latter parts are very simple to do using equations I have found on wikipedia, but Question A specifically asks "Determine the trajectory equation of the ball after being hit (give all the details from where the equation comes from)"

This is an 8 mark question so it seems to be quite in depth.

More background to the original problem;

A tennis player1 located on the line at the back of the court attempts to “lobe” his competitor. The tennis player2 stands 2 meters behind the net facing player1 who hits the ball in 0 (origin), 9 meters away from the net and at a height of h=0.5m above the ground. The tennis ball travels with a speed Vo=12 m/s, with the velocity vector at an angle = 60o with the ground.
g = 9.81 m/s2.


As I said, the rest of the coursework(questions B, C, D) are relatively simple and just asks you to solve some problems, which I can do using the equations I have found online.

However part A is really bothering me. I'm not sure how to go about constructing an equation and how to give details of how I arrived at it.

Any help would be much appreciated.

Welcome to the PF.

On trajectory questions like this, use the fact that the horizontal motion has a constant velocity (the horizontal component of the Vo you are given), if you can neglect air resistance slowing it down. The vertical motion follows a parabola defined by the y(t) equation for the motion given a constant acceleration (the downward acceleration of gravity g = 9.8m/s^2).

Can you now write those two equations?

 

[basedgod]

Can you now write those two equations?

I'm guessing x = T*Vcos60 for horizontal, but I am not sure for vertical. Also, I am not given any value for time.

Here are the rest of the questions in the coursework:

b. Give y = f(x) equation including the numerical parameters given.

c. Knowing that player 2 jumps, extending his tennis racket at the maximum, reaches a height of H=2.5m, do you think he will intercept the ball?

d. The rear tennis court line is 12m away from the net, will the ball be in? or will player1 fail?

I may have some problems with part B, but the other two questions are very simple if I use the equations already on wikipedia.

 

[berkeman]

I'm guessing x = T*Vcos60 for horizontal, but I am not sure for vertical. Also, I am not given any value for time.

Here are the rest of the questions in the coursework:

b. Give y = f(x) equation including the numerical parameters given.

c. Knowing that player 2 jumps, extending his tennis racket at the maximum, reaches a height of H=2.5m, do you think he will intercept the ball?

d. The rear tennis court line is 12m away from the net, will the ball be in? or will player1 fail?

I may have some problems with part B, but the other two questions are very simple if I use the equations already on wikipedia.

For the vertical motion y(t) you use an equation that relates y(t) to the initial vertical position y(0), plus a term including any initial vertical velocity Vy(t), plus a term including any vertical acceleration ay(t). Do you see an equation in your study materials that relates these terms?

 

[basedgod]

For the vertical motion y(t) you use an equation that relates y(t) to the initial vertical position y(0), plus a term including any initial vertical velocity Vy(t), plus a term including any vertical acceleration ay(t). Do you see an equation in your study materials that relates these terms?

I have had another look over my notes. I have come up with this for vertical motion: y = Yo + t (V*sin60) - 1/2*g*t^2 (yo = 0.5)

I don't know how to progress from here, as these equations don't help me out with the latter questions.

There is a section in my notes that shows how to eliminate T from these equations, but it is very confusing and doesn't really seem to get me to where I want to be.

 

[berkeman]

I have had another look over my notes. I have come up with this for vertical motion: y = Yo + t (V*sin60) - 1/2*g*t^2 (yo = 0.5)

I don't know how to progress from here, as these equations don't help me out with the latter questions.

There is a section in my notes that shows how to eliminate T from these equations, but it is very confusing and doesn't really seem to get me to where I want to be.

That is the correct equation for the vertical motion. Note that the last term is negative because the acceleration of gravity is downward, in the -y direction.

To procede on questions like this, I usually use the simpler horizontal motion equation to solve for the time of flight t, since you can usually figure out the horizontal distance from the problem statement, and Vy(t) is constant. Then use that value of t to solve for the vertical position when the ball reaches the far end of its trajectory.