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

In summary, the discussion is about finding the optimum angle for take off on a ski flying hill using projectile motion. The equations used to solve the problem involve time of flight, horizontal range, and the angle of launch. It is important to consider if the landing height is the same as the take off height when using these equations. If the landing height is different, the fundamental equations should be used instead.
  • #1
canycorns44
2
0

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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  • #2
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.)
 
  • #3
so how would I write it if the landing it different from the takeoff?
 
  • #4
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.
 

1. How do you determine the optimum angle for takeoff for a ski jump?

The optimum angle for takeoff for a ski jump is determined by a combination of factors, including the speed of the skier, the shape and condition of the jump, and the desired distance of the jump. This can be calculated using mathematical formulas and data collected from previous jumps.

2. What is the difference between the optimum angle for takeoff and the actual takeoff angle?

The optimum angle for takeoff is the angle that will result in the longest and most efficient jump. The actual takeoff angle is the angle at which the skier actually launches off the jump. These two angles may differ due to factors such as wind conditions, the skier's technique, and the accuracy of the calculations.

3. How does the shape of the ski jump affect the optimum angle for takeoff?

The shape of the ski jump plays a significant role in determining the optimum angle for takeoff. A steeper jump will require a higher takeoff angle to achieve the desired distance, while a flatter jump may require a lower takeoff angle. The shape of the jump also affects the speed and trajectory of the skier, which can impact the takeoff angle.

4. Is there a specific angle that is considered the "best" for ski jump takeoff?

There is no one specific angle that is considered the "best" for ski jump takeoff. The optimum angle will vary depending on the factors mentioned above, and may also differ for each individual skier. Coaches and athletes work together to find the most effective takeoff angle for each jump.

5. Can technology be used to determine the optimum angle for ski jump takeoff?

Yes, technology can be used to aid in determining the optimum angle for ski jump takeoff. High-speed cameras and specialized software can be used to analyze the skier's technique and track their trajectory, which can then be used to calculate the optimum angle for takeoff. However, human judgement and experience are still crucial in making the final determination of the takeoff angle.

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