Projectile Motion Problem This problem is completely evading me.

In summary, 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?
  • #1
Physics_Hates_Me
2
0
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?
 
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  • #2
Here's a picture just to help.

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

http://img158.exs.cx/my.php?loc=img158&image=0501252243177jy.jpg
 
  • #3
I think your answer is correct. Maybe the answer is supposed to be in radians?
 
  • #4
The answer should be roughly [itex] 0.114 rad [/itex] which is approx.the number you found (+6.5°).

Daniel.


P.S.How did you find 2 solutions??
 
Last edited by a moderator:
  • #5
dextercioby said:
The answer should be roughly [itex] 0.114 rad [/itex] which is approx.the number you found (+6.5°).

Daniel.


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

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

1. What is Projectile Motion?

Projectile motion is the motion of an object that is launched into the air at an angle or with an initial velocity. It follows a parabolic path due to the influence of gravity.

2. How do you solve a Projectile Motion problem?

To solve a projectile motion problem, you need to use the equations of motion, which take into account the initial velocity, acceleration due to gravity, and time. You also need to break the motion into horizontal and vertical components and use trigonometry to determine the angle and direction of the projectile.

3. What are the key factors that affect Projectile Motion?

The key factors that affect projectile motion are the initial velocity, angle of launch, air resistance, and the force of gravity. These factors determine the path of the projectile and how far it will travel.

4. How does air resistance affect Projectile Motion?

Air resistance can affect projectile motion by slowing down the object as it moves through the air. This can change the trajectory and distance the object travels. However, for most problems, air resistance is assumed to be negligible.

5. Can you provide an example of a Projectile Motion problem?

An example of a projectile motion problem would be a ball being thrown at an angle from the top of a building. The initial velocity, angle of launch, and height of the building would be given, and the goal would be to calculate the distance the ball will travel and the time it takes to reach the ground.

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