2. The speed v of an object being propelled through water is given by3(2PkC.v(P, C) =where P is the power being used to propel the object, C is the drag coefficient, andk is a positive constant. Swimmers can therefore increase their swimming speeds byincreasing their power or reducing their drag coefficients.To compare the effect of increasing power versus reducing drag, we need to somehowcompare the two in common units. A frequently used approach is to determine thepercentage change in speed that results from a given percentage change in power andin drag.If we work with percentages as fractions, then when power is changed by a fraction x(with x corresponding to 100x percent), P changes from P to P+xP. Likewise, if thedrag coefficient is changed by a fraction y, then C changes from C to C + yC. Then,the corresponding fractional change in speed isv(P+zР,С +УС) — v(Р,С)v(P,C) which then reduces to the function1+xf(x, y)1.+ y(a)Suppose that the changes in power x and drag y are small. Use thelinear approximation of f to describe the effect of a small fractional increase inpower versus a small fractional decrease in drag.(b)Based on the level curves of f(x, y) for the values c = -0.1,0, 0.1, 0.2, 0.3,what can you say about the speed if we increase the power P by 50% while thedrag C remains unchanged? What if we decrease the drag C by 50% while thepower P remains unchanged? What can you conclude from these changes?

Answered: Image /qna-images/answer/0f22a63c-9548-4d39-8bea-8824bcb8b35b.jpg

which then reduces to the function 1+x f(x, y) = 1. + y (a) Suppose that the changes in power x and drag y are small. Use the linear approximation of f to describe the effect of a small fractional increase in power versus a small fractional decrease in drag. (b) Based on the level curves of f(r, y) for the values c= -0.1,0,0.1,0.2, 0.3, what can you say about the speed if we increase the power P by 50% while the drag C remains unchanged? What if we decrease the drag C by 50% while the power P remains unchanged? What can you conclude from these changes?

which then reduces to the function 1+x f(x, y) = 1. + y (a) Suppose that the changes in power x and drag y are small. Use the linear approximation of f to describe the effect of a small fractional increase in power versus a small fractional decrease in drag. (b) Based on the level curves of f(r, y) for the values c= -0.1,0,0.1,0.2, 0.3, what can you say about the speed if we increase the power P by 50% while the drag C remains unchanged? What if we decrease the drag C by 50% while the power P remains unchanged? What can you conclude from these changes?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

The pilot of a Boeing 767 determines that a total of 22,300 kilograms of jet fuel is needed to fly from Montreal to Edmonton. A floatstick check finds that there is 11,133 litres of fuel already in the tanks. How much fuel, expressed in litres, must be added to the tanks? The density of jet fuel varies with temperature. For the prevailing conditions take the density of the jet fuel to be 0.803 kg/L or equivalently 1.77 lb/L.
To apply conservation of momentum to describe the motion of a rocket. A rocket is launched into deep space, where gravity is negligible. In the first second, it ejects 1/160 of its mass as exhaust gas and has an acceleration of 16.0 m/s2. What is vg, the speed of the exhaust gas relative to the rocket?
If a stream flowing at velocity U past a body of lengthL causes a force F on the body that depends only on U , L ,and fluid viscosity μ , then F must be proportional to(a) ρUL/μ, (b) ρU2L2, (c) μU/L, (d) μUL, (e) UL/μ
How much energy would it take to raise a can of soda (m = 350 grams) to average cruising altitude (35,000 ft)? Our textbook states that a gallon of gasoline contains 1.2×108 Joules of energy. Assuming 100% efficiency, how many gallons of gasoline would it take to raise the can of soda to 35,000 ft? A calorie is the amount of energy needed to raise the temperature of 1 gram of water by 1 Celsius degree (4.186 J). A nutritional Calorie is actually 1000 calories (1 Cal = 1 kcal). How many Calories of energy does it take to raise the can of soda to cruising altitude? Given that a can of Coke is about 140 Calories, how many cans of coke does it take to raise a can of coke to cruising altitude?
Resistance R to the motion of a completely submerged body is given by R = ρV2 L2 φ , where ρ and ν are density and kinematic viscosity of the fluid while L is the length of the body and V is the velocity of flow. If resistance of a one-sixth scale airship model when tested in water at 10 m/s is 230 N, what will be the resistance in air of the airship at the corresponding speed? Kinematic viscosity of air is 13 times that of water and density of water is 810 times of air.
Joan is setting up her new gaming PC, however she is worried about it overheating. She finds that the rate of heat loss (H), in W, that her cooling system can generate depends on the speed (V) and surface area (A) of her fans and the density of her coolant (ρ). Using the information provided above, determine the simplest expression that Joan can use to determine the rate of heat loss that her cooling system can generate.
S1: Frontal drag is a force that affects your acceleration when you glide. S2: When you glide you need to take off by kicking the wall of the pool to propel the body easily. A. Only the first statement is correct B. Only the second statement is correct C. Both statements are wrong D. Both statements are correct.
When rowing downstream consider the following scenario. The current of the water is moving at 2 m/s in the direction you are rowing. The coefficient of drag between your boat and the water is 1.2, the area in contact with the water is 0.1 m2 and the density of the water is 1000 kg/m3. You are moving at a velocity of 4 m/s into a head wind of 4 m/s. Your coefficient of drag between you and the air is 1.4, the area in contact with the air is 0.4 m2 and the density of the air is 1.2 kg/m3. Your goal is to create a net force moving downstream that is equal to 100 N. How much force must you exert with the oar and in what direction to achieve this net force downstream?
A block of mass m slides along a horizontal surface lubricated with a thick oil which providesa drag force proportional to the square root of velocity.F_d=-bv^1/2If v = v0 at t = 0, determine v as a function of time
A jet flights with a speed of 291 m/s . If the jet's engine has a power of 1,462,823 W. what is the air resistance? Calculate answer to one decimal
Three parallel plates are placed horizontally and are separated by two fluids at 18°C, with Plate A placed at the bottom and at rest, while Plate C is placed on top and moves at 3 m/s. Cyclohexane lies between Plate A and Plate B, spaced 3 cm apart, while water lies between Plates B and C spaced 3 cm apart. a. What is the relation of the rate of transfer of momentum between Plates A and B, with that between Plates B and C? b. Calculate the velocity of Plate B at steady state. c. Suppose that the plates are spaced equally 5-cm apart, what will be the velocity of Plate B and the shear stress exerted on Plate A to maintain Plate 3 at 3 m/s?
A ship displaces 7500cu.m of seawater with RD 1.025. what is its new displacement if its floating atthe same draft in water with RD 1.015?