# Projectile Motion Problem! This problem is completely evading me.

1. Jan 25, 2005

### Physics_Hates_Me

William Tell must split the apple atop his son's head from a distance of 27.8 m. When he aims directly at the apple, the arrow is horizontal. At what angle must he aim it to hit the apple if the arrow travels at a speed of 34.6 m/s?

This sounds extremely simple, and I thought I got the answer at first. However, the homework engine at my college keeps saying I got the answer wrong.

Here's how I did it:

Vyot - 1/2gt^2 = 0

I solve for t, and get t=0 and t=2Vyo/g

I plug the second t in the x-cordinate for horizontal motion.

R = x = Vxot = Vxo(2Vyo/g) = (2VxoVyo)/g = (2V^2o sin(theta)o cos(theta)o)/g)

Eh, the work is messy but I'll skip down to my final deriviation and that is:

sin 2(theta) = Rg/(velocity initial squared)
(This is a common formula and the book uses this same formula to solve similar problems like this. And the funny thing is that I can follow their answers using that equation, but I apparently don't get a correct answer when I'm using it in this problem.)

I plugged in all the information I got and received 6.58 degrees and 84.3 degrees. There are two answers, and I typed both of them in the homework engine, and it said they were wrong. What am I doing wrong?

2. Jan 25, 2005

### Physics_Hates_Me

Here's a picture just to help.

This is basically what I'm doing and I'm still apparently getting the wrong answer, lmao!

3. Jan 25, 2005

### learningphysics

4. Jan 26, 2005

### dextercioby

The answer should be roughly $0.114 rad$ which is approx.the number you found (+6.5°).

Daniel.

P.S.How did you find 2 solutions??

Last edited by a moderator: Jan 28, 2013
5. Jan 26, 2005

### learningphysics

Oops... I didn't notice the second solution he had. The 84.3 degrees is wrong. Is the computer expecting two answers?