Projectile motion, I cannot figure out how to do this

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Homework Help Overview

The problem involves projectile motion, specifically analyzing the trajectory of a football kicked at an angle of 50 degrees that lands 20 meters away horizontally. The vertical acceleration due to gravity is given as -9.81 m/s². The original poster seeks to determine the time the ball was in the air and the maximum height reached.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using trigonometric functions to resolve the initial velocity into horizontal and vertical components. There are mentions of setting up simultaneous equations based on the horizontal distance and vertical motion equations. Some participants question the correctness of the proposed methods and calculations, while others seek confirmation of their reasoning.

Discussion Status

The discussion includes various attempts to solve the problem, with some participants providing calculations for time and maximum height. There is a mix of agreement and disagreement regarding the methods used, and some participants express uncertainty about the correctness of their approaches. Guidance is offered on how to break down the problem into components, but no consensus is reached on a single method.

Contextual Notes

Participants note the importance of finding the initial velocity before proceeding with calculations. There is also a recognition of the need to clarify the distinction between total time in the air and time to reach maximum height.

deagle12
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Homework Statement



The problem is, "A footballer kicked a ball up at 50 degrees and it landed 20m away horizontaly", assuming vertical acceleration is -9.81ms-2 how would you find the time it was in the air and the max height reached.

How would you solve this?

Homework Equations





The Attempt at a Solution



Various trigonometric functions, if you need more detail please tell me.
 
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well you know that when it lands s_j =0
s0 s_i=20=v*cos(50) and S_j=0=vsin(50)t-9.81*.5*t^2
you now have a system of simultaneous equations... solve it
i get t=2.2s and v_init=14.11m/s
For max height.
at max height v_j=0
v_j=0^2=u^2+2as where u= vertical cmpt of v_init(14.11sin(50)) and a=-9.81,/s^2
0=(14.11sin(50))^2-2*9.81s solve
i get s=5.95m
 
can you let me know if this is right or useful please.
 
Well, first you have to have velocity, to even begin this. We know when it lands, it is going 0 m/s. So vf= 0 m/s. Now, once you find Vi, you will need to divide that up into vertical and horizontal components of velocity. (cos * theta, sin * theta)

Once you do that, you can find the time in air with
d=vft + 1/2at2

You have your horizontal distance, now solve for t.
I'm not sure you could use vf= vi + at could work for t, because of the lack of distance. But if you did use that, t would NOT BE THE TOTAL TIME IN THE AIR. It would be the time it takes to get to the max height of the projectile. So you would have to multiply it by 2.
 
No GreatEscapist that is not correct. Any high school physics text will tell you that all projectiles have a final velocity that is equal to the initial horizontal component + a vertical component relative to the acceleration(assuming no air drag). use the information i gave you it is correct.
 
Dang it. :P
Well, I tried. Sorry about that. At least now I know I need to brush up on my projectile motion. :S
 
Apart from the missing t here "s_i=20=v*cos(50)" , your solution is correct. Good job !

ehild
 

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