Concept explainers
(a)
Time at which Kathy overtakes Stan.
(a)
Answer to Problem 73AP
Kathy overtakes Stan at
Explanation of Solution
Kathy leaves the starting line
Write the expression for
Here,
Write the expression for the final position of Kathy’s car.
Here,
Write the expression for the final position of Stan’s car.
Here,
Since both the cars start from rest, their initial velocities are zero. That is
Use expression (I) in (V) to get
When Kathy’s car overtakes Stan’s car, the position of Stan’s car is equal to position of Kathy’s car. Therefore equate expressions (V) and (VI).
Expression (VII) is a quadratic equation.
Write the expression for finding the solution of (VII).
Conclusion:
Substitute
Therefore, Kathy overtakes Stan at
(b)
The distance travelled by Kathy before she catches Stan.
(b)
Answer to Problem 73AP
The distance travelled by Kathy before she catches Stan is
Explanation of Solution
Use expression (IV) to find the distance travelled by Kathy before catching him.
Conclusion:
Substitute
Therefore, the distance travelled by Kathy before she catches Stan is
(c)
The speed of both cars at the instant of overtaking of Stan by Kathy.
(c)
Answer to Problem 73AP
The speed of Kathy’s car is
Explanation of Solution
Write the expression for the final velocity of Kathy.
Here,
Write the expression for the final velocity of Stan.
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the speed of Kathy’s car is
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Chapter 2 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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