Calculating the Distance a Rock Travels Up a Sloped Hill

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In summary, the problem involves a rock approaching the foot of a hill with a speed of 16 m/s and a slope of 23 degrees. The goal is to calculate how far up the hill the rock travels. The equations used are KE = PE and mv^2/2 = mgy. It is important to take into account the angle of the slope and the fact that the hill is frictionless. A picture can also be helpful in visualizing the problem.
  • #1
eglaud

Homework Statement


A rock approaches the foot of a hill with a speed of 16 m/s. The hill has a slope of 23 degrees, how far up the hill does the rock travel?

Homework Equations


KE = PE

The Attempt at a Solution


I tried mv2/2 = mgy but I know this isn't right since I don't use theta at all. What do I do to change this?
 
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  • #2
Is the equation KE = PE - W? This is what I did before, but I am unsure why except that I can plug in the angle, but I forgot to include this HILL IS FRICTIONLESS so I wouldn't have thought to use this.
 
  • #3
eglaud said:

Homework Statement


A rock approaches the foot of a hill with a speed of 16 m/s. The hill has a slope of 23 degrees, how far up the hill does the rock travel?

Homework Equations


KE = PE

The Attempt at a Solution


I tried mv2/2 = mgy but I know this isn't right since I don't use theta at all. What do I do to change this?

Have you drawn a picture?
 
  • #4
RedDelicious said:
Have you drawn a picture?

Yes, it looks like a rock moving towards a triangle
 
  • #5
eglaud said:
how far up the hill does the rock travel?

eglaud said:
mv2/2 = mgy
Presumably your y is the vertical ascent, but I don't think that is quite what the question is asking for.
 
  • #6
Hello everybody. Sorry for my english. I am not native. I think you must calculate de kinetic Energy at the bottom of the hill. Then, you must calculate the position (dependent with the angle) at the velocity is 0 m/s.
 
  • #7
AgusCF said:
Hello everybody. Sorry for my english. I am not native. I think you must calculate de kinetic Energy at the bottom of the hill. Then, you must calculate the position (dependent with the angle) at the velocity is 0 m/s.
I think eglaud understands that but has not interpreted the question correctly. See my post #6.
 
  • #8
haruspex said:
I think eglaud understands that but has not interpreted the question correctly. See my post #6.
Ouch! Yeap you are right! And I think that the problem wants to calculate the distance that the rock goes up on the lateral of the hill.
 

1. How does a rock approach a hill?

A rock approaches a hill through the force of gravity. As the rock moves closer to the hill, it experiences an increasing gravitational pull towards the hill, causing it to move in that direction.

2. What factors affect the speed at which a rock approaches a hill?

The speed at which a rock approaches a hill can be affected by various factors such as the mass of the rock, the slope of the hill, and any external forces acting upon the rock.

3. Can a rock approach a hill from any angle?

Yes, a rock can approach a hill from any angle as long as it is within the range of the gravitational pull of the hill. However, the angle at which the rock approaches the hill can affect its trajectory and speed.

4. Will a rock always reach the top of a hill?

No, a rock may not always reach the top of a hill. The speed, angle, and mass of the rock, as well as the steepness and height of the hill, can all affect whether or not the rock will be able to overcome the gravitational pull and reach the top of the hill.

5. What happens when a rock reaches the top of a hill?

When a rock reaches the top of a hill, it will stop moving upwards and begin to roll or slide down the other side of the hill. This is because the gravitational pull is now pulling the rock in the opposite direction, towards the center of the Earth.

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