Find H: Ski Jump Physics Problem

In summary: Well, I think you need to consider the velocity of the skier when he leaves the ramp. mgH-mgh is the kinetic energy at that point, right? And if there is no drag, then the horizontal velocity at the time he leaves the ramp will be constant throughout the drop. Then you can use kinematics to solve for that x velocity, right? Use a system of kinematics equations(I think this is what you are missing) to get rid of time and I believe there is only one variable left: H.So in the x direction, I used the equation:\Delta x = v_{x}t+\frac {1}{2
  • #1
juggalomike
51
0

Homework Statement


A skier (m=53.00 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. If h = 8.00 m and D = 9.50 m, find H.
http://img517.imageshack.us/img517/616/prob21a.gif


Homework Equations


.5mv^2+mgh=.5mv^2+mgh


The Attempt at a Solution


I first divided to vertical distance by 9.81 to get .81seconds, then 9.50/.81 to get the horizontal velocity, which is 11.72 m/s

I then plugged the information into the above equation for

53*9.81*x=.5*53*11.72^2+53*9.81*8
solving for x i got 15.01 m, which is not correct.
 
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  • #2
Well, I think you need to consider the velocity of the skier when he leaves the ramp. mgH-mgh is the kinetic energy at that point, right? And if there is no drag, then the horizontal velocity at the time he leaves the ramp will be constant throughout the drop.

Then you can use kinematics to solve for that x velocity, right? Use a system of kinematics equations(I think this is what you are missing) to get rid of time and I believe there is only one variable left: H

EDIT: I get 10.82m for the answer. If that isn't correct, then the way I suggested might not be right.
 
Last edited:
  • #3
Brilliant said:
Well, I think you need to consider the velocity of the skier when he leaves the ramp. mgH-mgh is the kinetic energy at that point, right? And if there is no drag, then the horizontal velocity at the time he leaves the ramp will be constant throughout the drop.

Then you can use kinematics to solve for that x velocity, right? Use a system of kinematics equations(I think this is what you are missing) to get rid of time and I believe there is only one variable left: H

EDIT: I get 10.82m for the answer. If that isn't correct, then the way I suggested might not be right.
your answer was correct, thanks for the help but could you please tell me how you used kinematics to solve for velocity? after plugging the hight u gave me back into the energy equation i see the velocity was 7.44, which is way off from what i was getting.
 
  • #4
Yeah, of course.
So in the x direction, I used the equation:
[tex]
\Delta x = v_{x}t+\frac {1}{2}at^2
[/tex]
So in terms of this problem:
[tex]
D= v_{x}t
[/tex]
Because there is no acceleration.

In the y direction, I used the same equation, and in terms of this problem:
[tex]
h= \frac {1}{2}at^2
[/tex]
I left off the vt because there is no initial y velocity since the skier leaves the ramp horizontally.

I solved this for t and substituted it into the first equation, and then solved it for vx

I think you can finish it once you have this velocity.
 

1. What is the purpose of finding H in a ski jump physics problem?

The purpose of finding H in a ski jump physics problem is to determine the height of the ski jump. This is an important factor in calculating the velocity, distance, and other aspects of the jump.

2. How is H calculated in a ski jump physics problem?

H is typically calculated using the equation H = V2 / (2 * g * sin(θ)), where V is the initial velocity of the skier, g is the acceleration due to gravity, and θ is the angle of the ski jump.

3. What factors can affect the accuracy of the H calculation in a ski jump physics problem?

The accuracy of the H calculation can be affected by factors such as air resistance, the shape of the ski jump, and the condition of the snow. Other variables, such as the skier's technique and equipment, can also play a role.

4. How does the height of a ski jump impact the overall performance of a skier?

The height of a ski jump can greatly impact the overall performance of a skier. A higher jump can allow for a longer flight time and greater distance, but it also requires more speed and can be more challenging to land successfully.

5. Can the H calculation be used to predict the outcome of a ski jump competition?

The H calculation can provide valuable information for predicting the outcome of a ski jump competition, but it is not the only factor to consider. Other variables, such as wind conditions and the skier's technique, can also play a significant role in the final result.

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