Projectile motion with unknown angle and Vo

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Homework Help Overview

The discussion revolves around a projectile motion problem involving a footballer kicking a ball to reach a maximum height of 4 meters at a horizontal distance of 20 meters. Participants are tasked with determining the initial speed and angle of the kick, considering the ball as a material point.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion over the correct application of trigonometric equations and the use of symbols in their equations. There are discussions about the independence of vertical and horizontal motion components and the potential to simplify the problem by avoiding time in calculations. Some participants explore the implications of using different equations and the relationships between the variables involved.

Discussion Status

The conversation is ongoing, with participants providing guidance on how to approach the problem. Some suggest splitting the initial velocity into components and using known equations to relate the variables. There is recognition of multiple unknowns and equations, with participants attempting to clarify their understanding and resolve their confusion.

Contextual Notes

Participants note the presence of multiple unknowns (angle, initial velocities) and the challenge of using the correct equations. There is mention of a specific formula provided by a lecturer, which some participants question or express uncertainty about. The discussion reflects a mix of attempts to apply known physics principles and the need for clarification on the problem setup.

Femme_physics
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Homework Statement



http://img854.imageshack.us/img854/6055/footballer01.jpg

A footballer kicks a ball and therefor the ball arrives at point C, above the goal at 4 meters height

Presuming that point C is at max height of the path and distance AB is 20 meters, calculate the speed of the ball (Va - angle and magnitude) during the kick. Presume that the ball is a material point.

The Attempt at a Solution



I'm getting stuck. I'm not sure whether it's my issue with solving trigonometric equations, or have I not applied the correct method? This is the first time I find a projectile motion problem to be so tough!

http://img8.imageshack.us/img8/962/footballer02.jpg
 
Last edited by a moderator:
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You're mixing up your symbols.

In equation #2 you're using v0, while this should be vy.
That should make it (quite a bit) easier. ;)

EDIT: Btw, where did you get equation #4 from?
 
You're mixing up your symbols.

In equation #2 you're using v0, while this should be vy.
That should make it (quite a bit) easier. ;)

Hmm. I'll try it now then.
Geez...what a tough problem!

EDIT: Btw, where did you get equation #4 from?

This?

http://img852.imageshack.us/img852/3820/thisr.jpg

Uploaded with ImageShack.us

Our lecturer gave it to us. He seemed to be holding it as a really special great formula!
 
Last edited by a moderator:
The movement of the ball can be split in two indipendent components: one vertical and one horizontal.
Then you can mix them up in the end.

In addition you may know that almost every law is reversible in time: that means you can imagine someone throwing a ball at the top of the 4 meters pole and the ball has to reach the player.
 
In addition you may know that almost every law is reversible in time: that means you can imagine someone throwing a ball at the top of the 4 meters pole and the ball has to reach the player.

I don't appear to have a need for time. Adding time into the equations seem like extra work!

From what you're saying though, it appears that I'm making my life harder using the trajectory formula. Can I simply use the formulas of


http://img802.imageshack.us/img802/8066/3components.jpg


Wait, ignore that last equation. It should be V2=Vx2+Vy2
 
Last edited by a moderator:
Femme_physics said:
This?

Our lecturer gave it to us. He seemed to be holding it as a really special great formula!

Ah, I see.
I think it should be:

g \cdot h = \frac {v_0^2 \cdot \sin^2 \alpha} 2

That should give you the answer as well.
 
Just to keep tab, I got 3 unknowns (angle, vox and voy) and I can use 5 equations to try and solve it?

*also, I'm surprised he confused the formula! Or maybe I mis-copied it? Hmm...
 
Femme_physics said:
I don't appear to have a need for time. Adding time into the equations seem like extra work!

From what you're saying though, it appears that I'm making my life harder using the trajectory formula. Can I simply use the formulas of


http://img802.imageshack.us/img802/8066/3components.jpg


Wait, ignore that last equation. It should be V2=Vx2+Vy2

Ok, and how much time take for an object to fall from an height H under the acceleration of gravity g ?
 
Last edited by a moderator:
I just realized I accidentally added "time" into the equation
 
  • #10
Femme_physics said:
Just to keep tab, I got 3 unknowns (angle, vox and voy) and I can use 5 equations to try and solve it?

*also, I'm surprised he confused the formula! Or maybe I mis-copied it? Hmm...

Hmm, those other formulas are not quite right either.

It should be:

v_x=v_0 \cos \alpha
v_y=v_0 \sin \alpha - g \cdot tor

v_{0x}=v_0 \cos \alpha
v_{0y}=v_0 \sin \alpha
 
  • #11
Last edited by a moderator:
  • #13
Femme_physics said:
Just to keep tab, I got 3 unknowns (angle, vox and voy) and I can use 5 equations to try and solve it?

*also, I'm surprised he confused the formula! Or maybe I mis-copied it? Hmm...

Actually you have a 4th unknown: v0.

And yes, you can try and solve it.

I can also suggest another approach.
Split the initial velocity in a horizontal and a vertical component, and set up the equations for the horizontal and vertical distance and speed.

Up to you though.
 
  • #14
Last edited by a moderator:
  • #15
Before you were able to state that the ball takes 0.903 sec to reach the top.

At the top you also know the ball doesn't rise further, so Vy must be... ?
You know g, t, Vy when the ball is at the top, get a value for V_0 \ sin (\alpha)
using your equations.
 

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