Conservation of energy, ball kicked into a canyon

In summary, to find the maximum height reached by a ball kicked off a 100.0 m canyon at an angle of 30.0 degrees above the horizontal with a velocity of 24.0 m/s, you can use the conservation of energy formula and the knowledge that the vertical component of the velocity will be 0 at the ball's peak. Add this height to the initial height above the canyon to get the maximum height reached.
  • #1
lking226
20
0

Homework Statement


A ball is ikicked off a 100.0 m canyon at an angle of 30.0 degrees above the horizontal with a velocity of 24.0 m/s. What maximum height does it reach above the canyon floor?


Homework Equations


WNC = KE + PE


The Attempt at a Solution


WNC = 1/2mvf^2 - 1/2mvi^2 + mghf - mghi
1/2mvi^2 + mghi = 1/2mvf^2 + mghf

I'm not sure what to do with the 30.0 degree angle?
 
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  • #2
lking226 said:
I'm not sure what to do with the 30.0 degree angle?

You can find the horizontal and vertical component of the initial speed of the ball
with the angle. When the ball is at its highest point, the vertical component will be 0.
 
  • #3
lking226 said:

Homework Statement


A ball is ikicked off a 100.0 m canyon at an angle of 30.0 degrees above the horizontal with a velocity of 24.0 m/s. What maximum height does it reach above the canyon floor?


Homework Equations


WNC = KE + PE


The Attempt at a Solution


WNC = 1/2mvf^2 - 1/2mvi^2 + mghf - mghi
1/2mvi^2 + mghi = 1/2mvf^2 + mghf

I'm not sure what to do with the 30.0 degree angle?
You meant to say W_nc= delta KE + delta PE = 0, which is what you ended up with. When the ball reaches its max height, what is v_fy and what is v_fx?
 
  • #4
okay so after i have vix = 20.785 and viy = 12, what do i do with those?
 
  • #5
This is a projectile motion above a canyon. You've seem to have already found the vertical and horizontal components of the initial velocity so let's think about this some more.

In a projectile motion we're eventually going to reach a peak right?

Is there any specific property which notifies us that we've reached the peak of our projectile motion? (HINT: using the vertical/horizontal components of velcoity)
 
  • #6
the velocity in the y direction will equal 0.
 
  • #7
so i put that into the conservation of energy formula and solve for final height! thanks!
 
  • #8
lking226 said:
so i put that into the conservation of energy formula and solve for final height! thanks!

I'm not entirely sure if that's correct. You told me above that the vertical component of its velocity will be 0 when it reaches its maximum height during its projectile motion. Calcuate this height and add it to the height of the ball initially above the canyon.

That will give you its maximum height.
 

1. What is the conservation of energy?

The conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed, but it can be converted from one form to another. This means that the total amount of energy in a closed system remains constant.

2. How does conservation of energy apply to a ball kicked into a canyon?

When a ball is kicked into a canyon, it gains kinetic energy from the force of the kick. As it travels through the air, it also gains potential energy due to its position above the ground. When it reaches the bottom of the canyon, the ball has converted all of its kinetic and potential energy into thermal energy and sound energy, due to the force of impact and friction with the ground. This is an example of the conservation of energy in action.

3. What factors affect the conservation of energy in this scenario?

The conservation of energy in this scenario is affected by various factors such as the initial force of the kick, the mass and velocity of the ball, the height of the canyon, and the properties of the ground at the bottom of the canyon.

4. Is the conservation of energy always true in real-life situations?

While the conservation of energy is a fundamental principle, it may not always be true in real-life situations due to external factors such as friction, air resistance, and other forms of energy loss. However, the conservation of energy is still a useful concept in understanding and predicting the behavior of physical systems.

5. How is the conservation of energy related to other laws of physics?

The conservation of energy is closely related to other laws of physics, such as the law of conservation of momentum and the law of thermodynamics. These laws all describe the behavior of energy and matter in different contexts, but they all stem from the fundamental principle of the conservation of energy.

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