Concept explainers
(a)
To plot: The velocity-time graph and acceleration-time graph for given situation on a single graph.
(a)
Explanation of Solution
Given:
The free fall of the professor is for
Initial velocity of the professor is
The acceleration opposite to gravity applied after free fall is
The speed which is maintained until she reaches the ground is
Formula used:
Write expression for the final velocity of the professor during free fall.
Here,
The initial speed when she starts slowing her rate of descent will be same as the final velocity of the free fall.
Write expression for final speed of professor when she reaches
Rearrange above expression for
Here
Calculation:
Substitute
Substitute
The graph for the velocity and acceleration of the professor is shown in figure 1.
(b)
To find:The speed of professor at the end of first
(b)
Answer to Problem 102P
The speed of professor at the end of
Explanation of Solution
Given:
The initial speed of the professor is
The time of fall of the professor is
The acceleration due to gravity on the surface of earth is
Formula used:
The professor jumps out of the helicopter and falls freely under the action of acceleration due to gravity, the motion of the professor for these first
The first equation of motion relates the initial and final velocity of a body falling freely under the gravity. Therefore, the velocity of the professor can be obtained from this expression at the instant of
Write expression for the final velocity of the professor during free fall.
Calculation:
Substitute
Conclusion:
Thus, the speed of professor at the end of
(c)
To find: The duration for which the professor descends her speed.
(c)
Answer to Problem 102P
Explanation of Solution
Given:
The initial speed of the professor during descend is
The final speed of the professor at which time is measured is
The deceleration of the professor is
Formula used:
The time taken by the professor during her slow rate of descent can be obtained from Newton’s first equation of motion.
Write expression for final speed of professor.
Rearrange above expression for
Calculation:
Substitute
Conclusion:
Thus, the duration for which she descends her speed is
(d)
To find:Distance covered by the professor when she descends her speed.
(d)
Answer to Problem 102P
Explanation of Solution
Given:
The initial speed of the professor during descend is
The deceleration of the professor is
Formula used:
Write expression for final speed of the professor during the descent.
Rearrange above expression for
Calculation:
Substitute
The negative sign shows the direction of motion.
Conclusion:
Thus, the distance covered by the professor during the descent is
(e)
To find:Time required by the professor to reach the ground.
(e)
Answer to Problem 102P
Explanation of Solution
Given:
The altitude of helicopter is
Formula used:
Write expression for distance travelled during free fall of the professor.
Write expression for the distance covered when she maintains constant speed of
Here, S is the distance covered during constant speed motion.
Write expression for time taken to when professor maintained constant speed.
Write expression for total time of journey.
Calculation:
Substitute
Here, negative sign shows the direction of motion.
Substitute
Substitute
Substitute
Conclusion:
Thus, the total time taken by the professor for complete journey is
(f)
To find:The average velocity of professor for entire trip.
(f)
Answer to Problem 102P
Explanation of Solution
Given:
The distance through which the professor falls is
The time for which the professor falls is
Formula used:
Average velocity is defined as the ratio of total distance covered to the total time taken during the journey.
Write expression for average velocity of the professor.
Here
Calculation:
Substitute
Conclusion:
Thus, the average velocity of the professor is
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Chapter 2 Solutions
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