Concept explainers
(a)
To calculate: The skier’s vertical component of acceleration.
(a)
Answer to Problem 68GP
The vertical component of acceleration is
Explanation of Solution
Given data:
Acceleration,
The angle of slope of the hill with the horizontal,
Formula used:
The magnitude of vertical component of acceleration a is:
Calculation:
Consider the downward direction to be positive y direction.
The acceleration of the skier,
The angle of slope of the hill with the horizontal,
The vertical component of acceleration is directed downwards, and its magnitude is given by,
Conclusion:
The vertical component of acceleration is
(b)
To calculate: The time taken by the skier to reach the bottom of the hill.
(b)
Answer to Problem 68GP
The time taken by the skier to reach the bottom of the hill is
Explanation of Solution
Given data:
Acceleration,
The angle of slope of the hill with the horizontal,
Initial velocity,
Total displacement,
Vertical acceleration,
Formula used:
From laws of motion,
Where d is the total displacement of a body, u is initial velocity , t is total time of motion, and a is the acceleration of the body.
Calculation:
Consider the downward direction to be positive y direction.
Initial velocity,
Total displacement,
Vertical acceleration,
Therefore, from laws of motion,
Conclusion:
The time taken by the skier to reach the bottom of the hill is
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Physics: Principles with Applications
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