   Chapter 5, Problem 33P

Chapter
Section
Textbook Problem

A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?

To determine
The height of the hill.

Explanation

Given Info:

Combined mass of the child and sled is 50.0kg .

The speed of the sled at the bottom is 3.0m/s .

Since the sled is sliding down on a frictional less surface and no other non conservative forces are doing work. Consider the zero potential energy at the base of the hill.

According to conservation of mechanical energy,

12mvf2+mghf=12mvi2+mghi       (I)

• m is the mass of the child and the sled
• vf is the final velocity of the system
• g is acceleration due to gravity
• hf is the final height with base of the hill
• vi is the initial velocity of the system
• hi is the initial height of the system

Since the child is sling to the bottom of the hill,

hf=0

Equation (I) gives,

12mvf2

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