# Projectiles and conservation of energy (water slide problem)

• wmmk
In summary, the problem involves a person sliding down a frictionless water slide and landing in a pool. The task is to find the height of the slide, given that the person starts from rest at a height of 1.50 m and lands at a horizontal distance of 2.58 m from the base of the slide. Using the conservation of mechanical energy theorem and the kinematic equations, the height of the slide can be calculated by linking the energy and projectile portions of the problem.
wmmk

## Homework Statement

The water slide shown in the figure ends at a height of 1.50 m above the pool. If the person starts from rest at point A and lands in the water at point B, which has a horizontal distance L = 2.58 m from the base of the slide, what is the height h of the water slide? (Assume the water slide is frictionless.)

## Homework Equations

PEi+KEi+W=PEf+KEf
PE=mgh
KE=(1/2)mv2
Vertical displacement after leaving slide: Dy=vot+(1/2)at2
Horizontal displacement after leaving slide Dx=vft

## The Attempt at a Solution

PEi+KEi+W=PEf+KEf
PEi=KEf
mghi=(.5)mvf2
(9.81)h=(.5)vf2

I'm not really sure where to go from here. Any help would be greatly appreciated.
Thanks,
Will

well v would be v=√(2gh).

It looks like the person leaves the slide horizontally. Use the kinematic equations, you are given the range L.

First let's consider the energy part of the problem by setting up an coordinate frame such that y=0 at the bottom of the slide. From this you can apply the conservation of mechanical energry theorm PE1+KE1=PE2+KE2 which will result in PE1=KE2. This is because we defined y=0 at the base of the slide and thus PE2=0 with respect to that frame. Now let's look at the projectile part of the problem. We know how far the person traveled in the 1.5m from the ground to the base of the slide, and we can calcualte the time it takes an object to fall 1.5 under the influence of gravity. So we know distance in the x direction and the time it took to travel that distance, thus we know our x velocity Vx. Last we link the energy and projectile portions of the problem to obtain a solution. We can now do this because we know KE2 since we calculated that velocity Vx. If we know KE2 we know the potential energy PE1 at the top of the slide and thus the height.

Also note that work W should not appear in the conservation of mechanical energy equation. If you were referring to Wg the work due to gravity you doubled down on that term since Wg is already accounted for in terms of potential energy in the conservation of mechanical energy equation.

## 1. What is a projectile and how does it relate to the conservation of energy in the context of a water slide problem?

A projectile is an object that is launched into the air and moves under the force of gravity alone. In the context of a water slide problem, a projectile would be the person going down the slide. Conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a water slide problem, the potential energy of the person at the top of the slide is converted into kinetic energy as they slide down.

## 2. How does the height of the water slide affect the speed of the projectile?

The height of the water slide does not affect the speed of the projectile. The speed of the projectile is determined by the initial potential energy, mass, and the force of gravity acting on it. The height of the slide only affects the potential energy, not the speed.

## 3. What role does friction play in the conservation of energy in a water slide problem?

Friction plays a minimal role in the conservation of energy in a water slide problem. Frictional forces acting on the person going down the slide may cause some of the energy to be converted into heat, but this is a small amount compared to the overall energy transfer from potential to kinetic energy.

## 4. Can the conservation of energy equation be applied to a water slide problem?

Yes, the conservation of energy equation can be applied to a water slide problem. The equation states that the initial potential energy (mgh) is equal to the final kinetic energy (1/2mv^2). This equation can be used to calculate the speed or height of the projectile in a water slide problem.

## 5. How does the mass of the projectile affect the conservation of energy in a water slide problem?

The mass of the projectile does not affect the conservation of energy in a water slide problem. The conservation of energy equation only takes into account the mass of the object (m) and its velocity (v), not the actual weight of the object. Therefore, the mass of the projectile does not play a direct role in the conservation of energy in a water slide problem.

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