(a)
The velocity of the skier at the bottom of the valley.
(a)
Answer to Problem 18PP
Explanation of Solution
Given:
The velocity of a skier at the top of the first hill is
The height of the first hill from which a skier starts to move is
A skier skis down a
Formula used:
According to law of conservation of energy, the total energy is always conserved. This means that the system energy will always remain same.
Calculation:
Since the energy is conserved, the sum of kinetic energy and potential energy of a skier at the top of the first hill is equal to the sum of kinetic energy and potential energy of that skier at the bottom of the valley. This can written as,
Where,
Substituting these expressions in equation
g is the acceleration due to gravity,
Since the velocity of a skier at the bottom of the valley is to be determined, potential energy,
Substituting the numerical values in equation (3),
Conclusion:
The velocity of the skier at the bottom of the valley is
(b)
The skier’s speed at the top of the second hill.
(b)
Answer to Problem 18PP
Explanation of Solution
Given:
The velocity of a skier at the top of the first hill is
The height of the first hill from which a skier starts to move is
A skier skis down a
Height of the second hill is
Formula used:
According to law of conservation of energy, the total energy is always conserved. This means that the system energy will always remain same.
Calculation:
Energy equation for a skier moving from the top of the first hill to the top of the second hill can be written as,
Where,
Substituting these expressions in equation
Since
Substituting the numerical values in equation
Conclusion:
The skier’s speed at the top of the second hill is
(c)
To identify: Whether the angles of the hills affect the values obtained in part (a) and (b).
(c)
Answer to Problem 18PP
No, the angles of the hills will not affect the values obtained in part (a) and (b)
Explanation of Solution
As can be seen in the equations used to calculate speed of the skier at the bottom of the valley and top of the second hill, the gravitational potential energy of a skier at the top of the hill depends merely on the height of the hill. It does not depend on the angle of the hill or length of the pathway along the hill. Therefore the angles of the hills will not affect the velocity of a skier at the bottom of the valley and at the top of the second hill.
Chapter 11 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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