How to find the optimum angle for takeoff for ski jump using

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Homework Help Overview

The discussion revolves around determining the optimum angle for takeoff in ski jumping, specifically using principles of projectile motion. Participants are exploring the relationship between angle and horizontal range in the context of ski flying hills.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply projectile motion equations to find the optimum angle, questioning whether existing formulas suffice or if a new formula is needed. Some participants raise concerns about the assumptions related to takeoff and landing heights, prompting further inquiry into how to adjust calculations for different landing heights.

Discussion Status

The discussion is active, with participants questioning the assumptions made about the landing height in relation to takeoff. There is a suggestion to revisit fundamental equations to better understand the problem, indicating a productive direction in the exploration of the topic.

Contextual Notes

Participants are navigating the complexities of projectile motion equations, particularly in scenarios where the landing height differs from the takeoff height, which may affect the calculations and assumptions involved.

canycorns44
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Homework Statement


I need to find how to find the optimum angle for take off on the ski flying hill using projectile motion. and why?

Homework Equations


formula-for-trajectory-of-projectile-motion.png


The Attempt at a Solution


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I'm just confused, because would I just use all the formulas above to solve the problem? or do I have to create another formula?
The optimum angle would result in the maximum horizontal range, right?
We know the time of flight = 2Vyi/g so the range = Vxi*2Vyi/g = 2Vi²/g *sinΘ*cosΘ =
R(Θ) = 2Vi²/g *sinΘ*cosΘ = Vi²/g *sin2Θ
 
Last edited:
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The first and last equations you quote assume landing at the same height as take-off. Is that case in your question?
(Always best to quote the whole question word for word in your post, in case you have misinterpreted something.)
 
so how would I write it if the landing it different from the takeoff?
 
canycorns44 said:
so how would I write it if the landing it different from the takeoff?
Go back to the more fundamental ("SUVAT") equations from which those are derived.
 

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