Concept explainers
(a)
The maximum and minimum terminal speed for the skydivers.
(a)
Answer to Problem 39PQ
The maximum and minimum terminal speed of the skydivers are given below.
skydiver | Weight (N) | Length (m) | Radius (m) | Maximum (m/s) | Minimum (m/s) |
A | |||||
B | |||||
C |
Explanation of Solution
Write the formula for the terminal velocity of an object.
Here,
When the skydiver is pointing head down, the terminal velocity is maximum. The
Re-write the equation (I) for maximum terminal speed.
Here,
When the skydiver is pointing belly to earth, the terminal velocity is minimum. The
Re-write the equation (I) for minimum terminal speed.
Here,
Conclusion:
Substitute
Substitute
Similarly the maximum and minimum terminal speed of the skydiver B and C can be calculated.
The table below shows the maximum and minimum terminal velocity of the all three skydivers.
skydiver | Weight (N) | Length (m) | Radius (m) | Maximum (m/s) | Minimum (m/s) |
A | |||||
B | |||||
C |
(b)
The order in which the skydivers should leave the plane in order to form the formation.
(b)
Answer to Problem 39PQ
The order that should be followed to make the formation is C, B, A.
Explanation of Solution
To form the formation of the figure 6.1 all the divers at some point should reach together. Since the diver C has the lowest terminal speed, he should leave the plane first followed by diver B and last diver A.
In the order C, B and A, the divers B and A can initially travel head down to reach to the next divers. Then they can face the belly to down.
Conclusion:
The order that should be followed to make the formation is C, B, A.
(c)
The time that the first skydiver has to wait after jumping to join the formation. The change in waiting time for the first skydiver to join formation if it takes
(c)
Answer to Problem 39PQ
The time that the first skydiver has to wait after jumping to join the formation is
Explanation of Solution
The total wait time for the first skydiver is the total time required for the formation. It is equal to the time taken for the jump of skydiver B and A, then the time taken by the skydiver A to catch up with the skydiver C or the wait time for diver A.
The time gap between the divers to leave the plane is
Write the formula for the distance travelled by skydiver A.
Here,
Write the formula for the distance travelled by the skydiver C.
Here,
Since both the divers travel the same distance.
Re-write the above equation to get an equation for
Conclusion:
Substitute
Thus the total wait time for first skydiver is
If it takes if
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