Football Throw - Could be Relative Motion?

1. Feb 23, 2010

erok81

1. The problem statement, all variables and given/known data

Quarterback Fred is going to throw a pass to tight end Doug. Doug is 20 m in front of Fred and running straight away at 6.0 m/s when Fred throws the 500 g football at a 40 angle. Doug catches the ball without having to alter his speed and runs for the game-winning pass.

How fast did Fred throw the ball?

2. Relevant equations

Perhaps kinematics equations?

3. The attempt at a solution

I've been working on this one for about an hour and still can't seem to solve it. I've tried using the usual big three kinematics equations substiting all over the place, but I've missed the problem 4 times so far as I can't get the correct answer. I am guessing the 500g football doesn't matter in this problem?

Any ideas on this? Is it relative motion? I am completely stumped.

Last edited: Feb 23, 2010
2. Feb 23, 2010

erok81

Here is my best idea so far...

Using this kinematic equation: tex]s_f = s_i + v_i + \frac{1}{2} at^2[/tex]

For Fred the thrower solving for y-axis since I can use acceleration.

$$s_f = v_b sin\alpha + \frac{1}{2} at^2$$

Then for Doug the runner, using the same axis and equation.

$$s_f = s_i + v_i t$$

In order to catch both final positions have to be equal, so...

$$s_i + v_i t = v_b sin\alpha + \frac{1}{2} at^2$$

Then I tried plugging in all of the values and got the wrong answer.

Oh....I still end up with two unknowns. That's why I can't go any farther. Do I sub in something else to get rid of either the velocity or the time?

3. Feb 23, 2010

erok81

Ok next up since I have two variables.

Still using the ball thrower, I used another kinematic equation subbing it in for the t.

$$v_f = v_i +at$$

$$t= \frac{-v_b sin\alpha}{a}$$

Ended up with 70 something m/s. No way. :rofl:

4. Feb 23, 2010

Andrew Mason

It is not clear what the question is. Are you trying to find the speed at which the ball is thrown?

What you need are two expressions for time of flight.

Express time of flight in terms of range and horizontal speed of the ball. Also express it in terms of the range and the speed of the runner. See if you can solve it from that.

AM

5. Feb 23, 2010

erok81

Oh...maybe I should include that.

Here is the question, you are right. How fast did Fred throw the ball?

Am I on the right track using those kinematic equations? I think I just might be messing up the algebra somewhere.

Actually, I think I'll give it another try with the x-axis like you mentioned, instead of the y like I was.

6. Feb 23, 2010

Andrew Mason

The ball has to catch up to the player, which means it has to cover 20 m more than the player does during the time of flight.

Write out the expression for that time as I have suggested.

The range is given by:

$$R = v_{ball}^2\sin(2\theta)/g$$

That should give enough to solve for R and v_ball

AM

7. Feb 23, 2010

joshmdmd

Since this is projectile motion find the horizontal component first.. ignore the angle, mass and vertical for now. Try to use 2 formulas and combine em'

Then use trig to find the v1

8. Feb 23, 2010

erok81

Ok...I still don't get it, sorry.

I've been trying to solve it horizontal, vertical, and even a combo of both.

No matter what I try I either end up with huge numbers or two variables. Looking at that range formula I don't know R or v and can't figure out what to sub in to get one variable.

9. Feb 23, 2010

Andrew Mason

You have not tried writing out the expression for time of flight.

$$t = d/v = R/v_{ball}\cos\theta = (R-20)/v_{player}$$

This is the expression for range, R:

$$R = v_{ball}^2\sin(2\theta)/g$$

You have two unknowns: v_ball and R. you have two equations. See if you can do the algebra to work it out.

AM

10. Feb 24, 2010

erok81

It's not from lack of trying, that's for sure. This is about three hours I've spent on this so far. :rofl:

Sorry for the complete ignorance on the subject, we didn't cover this what-so-ever in class so I am trying to learn as I go.

11. Feb 24, 2010

erok81

Thank you, thank you, thank you.

I tried until about midnight last night and made some stupid error I didn't realize until the moment I went to bed - good ol' cancelling terms around +/- signs in a fraction. So first thing this morning I tried again...and got it! What a relief.

Without you guys helping me, I would never have gotten it.

This was trick; both of you were hinting on it, but I didn't pick it up.

$$t = d/v = R/v_{ball}\cos\theta = (R-20)/v_{player}$$

Some of the tricks to solve these things...

Thanks again!

Our professor said related rates weren't that important and completely skipped the subject. So this topic was definately neglected.