Projectile motion-range calculation

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SUMMARY

The discussion focuses on calculating the range of a projectile launched from an inclined surface, specifically a hill at angle α. The formula for range is given as R = (u² sin 2θ) / g, with additional considerations for the angle of launch β and the slope of the hill. Participants emphasize the importance of resolving the initial velocity into vertical and horizontal components to determine the distance traveled along the slope. The conversation highlights the need for a labeled diagram to visualize the problem and guide the calculations.

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  • Understanding of projectile motion principles
  • Knowledge of trigonometric functions and their applications
  • Familiarity with algebraic manipulation of equations
  • Ability to interpret and create labeled diagrams for physics problems
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  • Study the derivation of the range formula for projectile motion on inclined planes
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Apleo
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Warning! Posting template must be used for homework questions. Effort must be shown in the Attempt at a Solution.
1. the surface of a hill is inclined at α to horizontal,a stone is thrown from the top of the hill at initial speed u at angle β with vertical line. How far from the top will the stone strike the ground?

2. R=(u^2 sin2θ)\g or by rotational co ordinate geometry3. can't prove that the dist covered by the stone is 2(u^2 sinβcos(α-β))\gcos^2 α
 
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How did you go about trying to solve this? Where is your labelled diagram ?

The provided answer is correct, it's the distance measured along the sloping ground
 
Last edited:
shall i send you a labelled diagram
 
How shall i start the calculation?
 
Apleo said:
shall i send you a labelled diagram
Attach a jpeg to your forum post.
 
the curve of projectile is not perfect...if you cannot understand please ask! AND sorry for late reply!
 

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The launch velocity can be shown resolved into 2 components.

The time taken to cover distance CB can be established.
 
i had tried but got stuck!
 
Apleo said:
i had tried but got stuck!
Show the working of your attempt.
 
  • #10
i had got confused with it because the projectile had exceeded its range so i can't solve it , i just checked mine calculation its wrong so suggest me how to start!
 
  • #11
It has to be worked using algebra, as no numerical data is provided.

Can you resolve the launch velocity into vert and horiz components?

Using your diagram, CB is the horizontal distance the projectile travels, because after traveling for that time & distance it hits terrain.
 
  • #12
yes i had resolved it into vert & hoz components...but after that what should i do?
 
  • #13
"
Apleo said:
yes i had resolved it into vert & hoz components...
Well, what is your answer---how do you express the components of its initial velocity?
 
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