Help Me Hill Height for 35kg Child on 5kg Sled

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In summary, a 35-kg child on a 5-kg sled goes down a hill and reaches a speed of 30 km/h at the bottom. The hill has an angle of 25 degrees with the horizontal and the problem asks for the height of the hill. Using conservation of energy, the formula 0.5m(v)^2 = mgh can be used, with the appropriate units for velocity, to solve for the height of the hill. The mass of the child and sled, as well as the angle of the hill, are not necessary for solving the problem.
  • #1
GalacticSnipes
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Homework Statement


A 35-kg child goes down a hill on a 5-kg sled. Starting from rest, she reaches a speed of 30 km/h at the bottom of the hill. The hill makes an angle of 25 degrees with the horizontal.

(a) Assuming there is no heat generated by friction and air resistance, how high is the hill?

I don't really know how to solve this problem, help, please?
 
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  • #2
Are you familiar with conservation of energy?
What form of energy does the child have at the bottom of the hill? Where did this energy come from?
Hint: In this case, the mass of the child and sled and the angle of the hill aren't required to find the answer (as long as you work symbolically and don't try to plug any numbers in until the very end, which is generally the best approach)
 
  • #3
I am familiar with COE and I think it has KE at the bottom of the hill...?
 
  • #4
GalacticSnipes said:
I am familiar with COE and I think it has KE at the bottom of the hill...?

Correct. And do you know the formula for KE? What form of potential energy did the sled start with? Do you know the formula for that form of energy?
 
  • #5
would the whole formula be something like this: 0.5m(v)^2 = mgh?
 
  • #6
GalacticSnipes said:
would the whole formula be something like this: 0.5m(v)^2 = mgh?

Correct. Good work. Be sure to use the appropriate unit for velocity, a conversion in necessary.
 
  • #7
ok, thx
 

1. What is "Help Me Hill Height"?

"Help Me Hill Height" refers to the height of a hill or slope that is safe and appropriate for a 35kg child to sled down while sitting on a 5kg sled.

2. Why is it important to consider "Help Me Hill Height" for a 35kg child on a 5kg sled?

It is important to consider "Help Me Hill Height" because sledding down a hill that is too steep or too high can be dangerous for a child. This can increase the risk of accidents and injuries.

3. How do you determine the appropriate "Help Me Hill Height" for a 35kg child on a 5kg sled?

The appropriate "Help Me Hill Height" can be determined by considering the weight of the child and the sled, as well as the slope of the hill. It is recommended to choose a hill with a gentle slope and gradually increase the height as the child gains more experience and confidence.

4. Are there any other factors to consider when choosing the "Help Me Hill Height" for a 35kg child on a 5kg sled?

Yes, it is also important to consider the condition of the hill, such as the presence of obstacles or icy patches, as well as the weather conditions. It is also recommended to have adult supervision and proper safety gear, such as a helmet, when sledding.

5. Can the "Help Me Hill Height" be adjusted for different weights and sled sizes?

Yes, the "Help Me Hill Height" can be adjusted based on the weight of the child and the size of the sled. It is important to always choose a hill that is appropriate and safe for the child and the equipment being used.

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