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
Want to see more full solutions like this?
Chapter 6 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- (a) Estimate the terminal speed of a wooden sphere (density 0.830 g/cm3) falling through air, taking its radius as 8.00 cm and its drag coefficient as 0.500. (b) From what height would a freely falling object reach this speed in the absence of air resistance?arrow_forwardA Wall of Death is a carnival show featuring a motorcyclist rides along the vertical wall of the cylinder and performs various stunts while doing so. Given that the radius of the cylinder is 7 m and the static coefficient of friction is 0.8, what is the minimum speed in m/s2 that the motorcyclist must do to prevent the motorcycle to slip from the wall?arrow_forwardA small block with mass m is set on the top of an upside-down hemispherical bowl. If the coefficient of static friction between the block and the bowl is μs and the block is slowly repositioned at different points down the surface of the bowl, at what angle measured from the vertical will the block begin to slide? Write your answer in terms of the mass, m; the gravitational acceleration on Earth, g; and the coefficient of static friction, μs. (Assume the +y axis is vertically upward.)arrow_forward
- A car travels at a constant speed of 25.5 mi/h (11.4 m/s) on a level circular turn of radius 43.0 m, as shown in the bird's-eye view in figure a. What minimum coefficient of static friction, ?s, between the tires and the roadway will allow the car to make the circular turn without sliding?arrow_forwardA child places a picnic basket on the outer rim of a merrygo- round that has a radius of 4.6 m and revolves once every 30 s. (a) What is the speed of a point on that rim? (b)What is the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to stay on the ride?arrow_forwarda. Consider a man running through the equator, with what velocity (direction and magnitude) shouldhe run so that he attain the minimum possible weight? Please explain understandably.b. A wheel on an extremely low friction slanted surface will slide without rotating. However, if thesame surface is rough and having some friction the wheel will roll down (with rotation). Explainwhy and how, using free body diagram.arrow_forward
- A curve of radius 1.80x102 m is being designed in a new highway to allow cars travelling at 70.0 km/h to round the curve with zero frictional forces. a) At what angle must the road be banked? b) What is the minimum coefficient of friction that will allow a car to successfully go around the curve at 30.0 km/h?arrow_forwardA curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s.(a) What banking angle should you specify for this curve?(b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750 kg car going around the curve at the proper speed?arrow_forwardIn the figure, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 284 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?arrow_forward
- A child places a picnic basket on the outer rim of a merry-goroundthat has a radius of 4.6 m and revolves once every 30 s. (a) What is the speed of a point on that rim? (b) What is the lowest value of the coefficient of static friction between basket and merrygo-round that allows the basket to stay on the ride?arrow_forwardH.W: A pilot in a fast jet aircraft loops the loop. The radius of the loop is 400 m, and the aircraft has a speed of 150 m/s when it passes through the bottom of the loop. What is the apparent weight that the pilot feels; in other words, what is the force with which she presses against her chair? Express the answer as a multiple of her normal weight.arrow_forwardImagine a Ferris wheel that rotates three times each minute and has diameter of 19.4m. a) What is the centripetal acceleration of a rider? b) What force does the seat exert on a 36.6kg rider at the lowest point of the ride? c) What force does the seat exert on the rider at the highest point of the ride? d) When the rider is halfway between top and bottom, what is the angle that the force exerted by the seat on the rider makes with the vertical? e) What is the magnitude of the force exerted by the seat on the rider when the rider is halfway between top and bottom?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning