Question

A child of mass m starts from rest and slides without friction from a height h along a slide next to a pool (Fig. P8.27). She is launched from a height h/5 into the air over the pool. We wish to find the maximum height she reaches above the water in her projectile motion. (a) Is the child–Earth system isolated or

Non-isolated? Why? (b) Is there a non-conservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide. (d) Express the total energy of the system when the child is at the launching point. (e) Express the total energy of the system when the child is at the highest point in her projectile motion. (f) From parts (c) and (d), determine her initial speedat the launch point in terms of g and h. (g) From parts (d), (e), and (f), determine her maximum airborne height in terms of h and the launch angle. (h) Would your answers be the same if the waterslide were not frictionless? Explain.

Short answer

Answer

(a) Yes, the child-Earth system is isolated.

Step-by-step solution

Step-by-step-solutionStep 1:

In the absence of non-conservative forces, the law of conservation of energy states that the sum of the kinetic and potential energy of the system remains constant.

The potential energy is given as:

u=mgh

The kinetic energy is given as:

$k=\frac{1}{2}m{v}^2$

Where,

k= Kinetic energy

U= Potential energy

m= Mass of body

g= Gravitational acceleration

h= Height

Given Data

The height of the slide:h

The height of launch:$\frac{h}{5}$

Step 3:Part (a)

An isolated system is a system on which no non-conservative forces act. Therefore, as no dissipative forces are considered in the question, the system is an isolated system.