Conservation of energy and height of projectile

In summary, the conversation is about solving a physics problem involving a child sliding down a curved water slide and determining her maximum airborne height using conservation of energy. The person asking for help is struggling with word problems, but is on the right track with their calculations. There is a discussion about a possible error in the last equation and the concept of conservation of energy in the problem is mentioned.
  • #1
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A child slides without friction from a height h along a curved water slide (Fig. P5.44). She is launched from a height h/5 into the pool. Determine her maximum airborne height y in terms of h and . (Use q for and h as appropriate.)
p5_44.gif

I understand that you use conservation of energy to solve the problem, but for some reason my brain is dead to physics today. O-chem/Calc 1/Bio I can handle but for some reason these word problems are really tripping me up.

Here's what I have so far.

W(nc) =(KEf + PEf) - (KEi + PEi)
0 = 1/2mv^2 + mg(h/5) - (0 + mgh) (For the end of the slide to find velocity when she leaves slide)
ymax = vo^2sin^2(q) /(2 g)

Am I on the right track?
 
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  • #2
yes it is looking good, except i think you have some typo's in the last equation line, but i know what you mean.
 
  • #3
I ended up with ymax = (-h/5 + h)*(sin(q))^2 and its registering as incorrect. Notice any errors?
 
  • #4
how did you get (-h/5 + h)? I'm not getting that from using the energy equation solving for v.
 
  • #5
u've got it wrong- it's conservative since it's frictionless
 

Related to Conservation of energy and height of projectile

1. What is the Law of Conservation of Energy?

The Law of Conservation of Energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. How does the Conservation of Energy apply to the height of a projectile?

When a projectile is launched, it possesses kinetic energy due to its motion and potential energy due to its position. As the projectile rises, its kinetic energy decreases as it moves against gravity and its potential energy increases. At the highest point of the projectile's trajectory, all of its kinetic energy has been transformed into potential energy. As it falls back to the ground, the potential energy is converted back into kinetic energy.

3. Can the height of a projectile be increased by adding more energy?

Yes, according to the Law of Conservation of Energy, adding more energy to a projectile will increase its height. This can be achieved by increasing the initial velocity of the projectile or by increasing the force of the launch mechanism.

4. Is it possible for a projectile to have a constant height?

No, it is not possible for a projectile to have a constant height. As explained by the Law of Conservation of Energy, the projectile's energy will continuously transform between kinetic and potential energy as it moves through its trajectory. However, in the absence of external forces such as air resistance, the projectile's total energy will remain constant.

5. How does air resistance affect the conservation of energy and height of a projectile?

Air resistance, or drag, acts as an external force on a projectile and can affect the conservation of energy and height. As the projectile moves through the air, it experiences a resistance force that opposes its motion, resulting in a loss of kinetic energy. This means that the projectile will not reach the same height as it would without air resistance. Additionally, air resistance can also affect the trajectory of the projectile, causing it to deviate from its intended path.

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