Solve Downhill Problem: Find Distance of b with a=35m and theta=43.6

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Homework Statement

A man is at rest at the top of a hill ready to ski downwards. Find the distance of b which is his landing point in terms of a and theta. You may neglect all frictional effects, ground and air. If a = 35 m and theta = 43.6, estimate the value of b. Keep in mind that this man has started at rest and just coasts.

Homework Equations

Since this isn't necessarily a standard "type-of-question-which-one-would-use-a-specific-set-of-equations-for", I would say any kinematics equations would be relevant.

The Attempt at a Solution

I know that vi = 0 m/s. When I look at the diagram I'm thinking of splitting this problem into three sections, I sort of see three triangles formed. One at the start which the skiier is on the hypotenuse of, then there's a ditch triangle, then the final triangle with b. But I have no idea how to start with the first triangle.

If anyone has a better strategy or knows a better strategy that would be great or can help me start or anything. Thanks.

 

[Bhumble]

Since the problem states to ignore friction you really only have one section as long as you know that U + K = E.
The downhill then uphill section translates into an amount of kinetic energy being "launched" at angle theta (assuming those angles are suppose to be the same although they don't look like it at all). To determine his landing you need to determine how long he will be airborne, so just the y-component of the jump (so just determine the y-component velocity and keep in mind that gravity is pulling the skiier down). Then after you have the time you can determine the total x distance traveled in that time. After you have your two components just use the Pythagorean theorem to get the distance b.

 

[ashishsinghal]

If anyone has a better strategy or knows a better strategy that would be great or can help me start or anything. Thanks.

ok...you can easily find the velocity at the point it takes off. Then you take x-axis along the snow and y-axis perpendicular to it. Resolve g in these axis and solve. You will get the answer. But for that you need to have one more information which is not clearly given but is suggested in the figure you gave - Is the part of the hill from where he takes off and part where he lands perpendicular to each other.

 

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Since the problem states to ignore friction you really only have one section as long as you know that U + K = E.
The downhill then uphill section translates into an amount of kinetic energy being "launched" at angle theta (assuming those angles are suppose to be the same although they don't look like it at all). To determine his landing you need to determine how long he will be airborne, so just the y-component of the jump (so just determine the y-component velocity and keep in mind that gravity is pulling the skiier down). Then after you have the time you can determine the total x distance traveled in that time. After you have your two components just use the Pythagorean theorem to get the distance b.

Okay, so I can find the time using for the entire distance but I'm not sure how you get specificlly distance b, seems like you get the horizontal distance for the entire hill.

ok...you can easily find the velocity at the point it takes off. Then you take x-axis along the snow and y-axis perpendicular to it. Resolve g in these axis and solve. You will get the answer. But for that you need to have one more information which is not clearly given but is suggested in the figure you gave - Is the part of the hill from where he takes off and part where he lands perpendicular to each other.

What do you mean by 'g', and how do you easily find the velocity at the point it takes off? I only know the vi = 0m/s? And I'm not sure how the perpendicular thing comes into play?

 

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Any help?