Concept explainers
(a)
The speed of the car at the edge of the cliff.
(a)
Answer to Problem 77AP
The speed of the car is
Explanation of Solution
Draw the below figure as per given instruction.
The car has acceleration while it is on the slope and a different acceleration when it is falling. Take the motion apart into two different sections.
A chunk of motion is during the acceleration stays constant. The acceleration will change instantaneously at the brink of the cliff. The velocity and the position must be the same just before point
From point
Write the expression for position along the incline plane as.
Here,
Conclusion:
Substitute
Solve and rearrange the above expression in terms of
Thus, the speed of the car is
(b)
The elapsed time interval.
(b)
Answer to Problem 77AP
The time elapsed time interval is
Explanation of Solution
Use first equation of motion for the time interval.
Write the expression for motion in straight line as.
Here,
Rearrange the above equation in terms of
Conclusion:
Substitute
Thus, the time elapsed time interval is
(c)
The velocity of the car.
(c)
Answer to Problem 77AP
The velocity of the car is
Explanation of Solution
Initial velocity is same as final velocity as horizontal acceleration is zero for uniform velocity. The velocity can be written as initial and final velocity component.
Write the expression for final velocity along horizontal as.
Here,
Write the expression for initial velocity along vertical as.
Here,
Write the expression for final velocity in
Here,
Rearrange the above expression as final velocity as.
Write the expression for total velocity for the whole distance as.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Thus, the velocity of the car is
(d)
The total time interval the car is in motion.
(d)
Answer to Problem 77AP
The time interval for the total journey is
Explanation of Solution
Refer to drawn figure, the total time interval can be written as the sum of time required to cover distance
Write the expression for total time interval as.
Here,
Write the expression for time required to cover distance
Conclusion:
Substitute
Substitute
Thus, the time interval for the total journey is
(e)
The position of the car.
(e)
Answer to Problem 77AP
The horizontal distance covered by the time
Explanation of Solution
Write the expression for horizontal distance in time
Conclusion:
Substitute
Thus, the horizontal distance covered by the time
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Chapter 4 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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