
Concept explainers
(a)
Find the horizontal displacement of the dart as a function of initial speed.
(a)

Answer to Problem 78PQ
The horizontal displacement of the dart as a function of initial speed is
Explanation of Solution
Write the
Here,
Here,
Conclusion:
Substitute
The above equation is a quadratic and the solution for time will be,
Since time should be position take the positive root then the value of time is,
Substitute
Therefore, the horizontal displacement of the dart as a function of initial speed is
(b)
Find the horizontal displacement with initial velocity of
(b)

Answer to Problem 78PQ
The horizontal displacement with initial velocity of
Explanation of Solution
Use the horizontal displacement equation derived in previous part.
Conclusion:
Substitute
Therefore, the horizontal displacement with initial velocity of
(c)
Find the horizontal displacement with initial velocity of
(c)

Answer to Problem 78PQ
The horizontal displacement with initial velocity of
Explanation of Solution
Use the horizontal displacement equation derived in previous part.
Conclusion:
Substitute
Therefore, the horizontal displacement with initial velocity of
(d)
Drive the simplified expression for horizontal displacement for small initial velocity.
(d)

Answer to Problem 78PQ
The simplified expression for horizontal displacement for small initial velocity is
Explanation of Solution
When the initial velocity is small then the square of the initial velocity is negligible then equation III becomes.
Therefore, the simplified expression for horizontal displacement for small initial velocity is
(e)
Drive the expression for horizontal displacement for high initial velocity.
(e)

Answer to Problem 78PQ
The expression for horizontal displacement for high initial velocity is
Explanation of Solution
When the initial velocity is high then the
Therefore, the expression for horizontal displacement for high initial velocity is
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Chapter 4 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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