# 2D kinematic problem: Tennis serve

1. Mar 19, 2017

### williamwong0402

1. The problem statement, all variables and given/known data
Serving at a speed of 170 km/h a tennis player hits the ball at a height of 2.5 m and an angle θ below the horizontal. The service line is 11.9 m from the net, which is 0.91 m high. What is the angle θ such that the ball just crosses the net? Will the ball land in the service box, whose out line is 6.40 m from the net? [ANS: 6. 1°]

2. Relevant equations
Vy2=Voy2-g(y-y0)
y=y
0+½(Vy+V0y)t
x=x0+V0xt

3. The attempt at a solution
http://blob:https://www.physicsforums.com/e28d4bae-4e89-4ed3-a5bb-353215f729f5 [Broken]

Please let me know what is the problem in the solution.
i don't know how to find the answer [6.1°]

Last edited by a moderator: May 8, 2017
2. Mar 19, 2017

### lewando

v = 170 km/h or m/s?

3. Mar 19, 2017

### hndalama

how did you get t=0.534s? as far as I can tell, time is unknown?

you need to convert 170km/h into m/s.

from step 1, it looks like you've made the assumption that vfy=0, but there is no reason to think that the ball would have 0 velocity by the time it got to the net or floor.
Did you post a second picture below the first one that shows step 1? If you did, it's not showing, perhaps try posting it again.

Last edited: Mar 19, 2017
4. Mar 19, 2017

### williamwong0402

yes , i made a mistake , it is 170km/h

5. Mar 19, 2017

### williamwong0402

the given has X=11.9m /Y=1.4m / V=170km/h g=-9.81
i don't know how can find y0y or t
i didn't, just one picture

6. Mar 19, 2017

### hndalama

The question is asking us to solve for θ.
First I would convert the velocity 170km/h to m/s, then resolve this into its horizontal and vertical components. They will be in terms of θ.
Then use kinematic equations and the given information to derive an equation in terms of θ. Then the plan is to solve for θ.

Last edited: Mar 19, 2017
7. Mar 19, 2017

### haruspex

Is that supposed to be 2.5m-0.91m?

8. Jun 17, 2017

### midgic

I'm wondering about this question also. It's a question from the OpenStax AP Physics textbook. I have two equations with two unknowns (theta and t) and I'm not sure how to proceed.

9. Jun 17, 2017

### haruspex

I can neither verify your equations nor suggest how to proceed without seeing them.

10. Jun 17, 2017

### midgic

The initial velocity is 47.2 m/s

y-component: $$0.91 = 2.5 - 47.2*sin(\theta)*t - 4.9*t^2$$

x-component: $$11.9 = 47.2*cos(\theta)*t$$

So, we have two equations and two unknowns (theta and t), but I don't see how to proceed from here.
I would appreciate any help. Thanks a lot.

11. Jun 17, 2017

### haruspex

You can use the standard procedure for solving simultaneous equations: use one equation to express one unknown in terms of the other and use that to substitute for that first unknown in the other equation.
You have two equations to choose from for that first step, and two choices of which way to do the substitution. One of the four choices is easier than the others.

12. Jun 17, 2017

### midgic

Thanks a lot for your reply. This is what I tried:

$$t = \frac{11.9}{47.2*cos(\theta)}$$

$$0.91 = 2.5 - 11.9*tan(\theta) - \frac{4.9*(11.9)^2}{(47.2*cos(\theta))^2}$$

But I'm not sure how to solve the final equation for theta.

13. Jun 17, 2017

### haruspex

Good choices.
Next, it helps to know the quadratic relationship between tan and sec.

14. Jun 17, 2017

### midgic

Oh, thanks for pointing this out. Then I think I can put the equation in this form:

$$a*tan^2(\theta) + b*tan(\theta) + c = 0$$

Then I would use the quadratic formula to solve for tan(theta)?
Is this the standard way to solve a question like this?
Is there not a simpler way to find theta and time t?

In any case, thanks a lot for your help.

15. Jun 17, 2017

### haruspex

Yes.
I very much doubt it.