6.055J/2.038J (Spring 2010)Homework 4Do the following problems. Submit your answers and explanations online by 10pm on Wednesday, 10 Mar2010.Open universe: Collaboration, notes, and other sources of information are encouraged. However, avoidlooking up answers to the problem, or to subproblems, until you solve the problem or have tried hard. Thispolicy helps you learn the most from the problems.Homework is graded with a light touch: P (made a decent effort), D (made an indecent effort), or F (did notmake an effort).Problem 1 BandwidthTo keep your divide-and-conquer muscles strong, here is an exercise from lecture: Estimate thebandwidth of a 747 crossing the Atlantic filled with CDROMs.10±bits/s or 10. . .bits/sProblem 2 Gravity versus radiusAssume that planets are uniform spheres. How does g, the gravitational acceleration at the surface,depend on the planet’s radius R? In other words, what is the exponent n ing ∝ Rn? (1)±or. . .Problem 3 Gravity on the moonThe radius of the moon is one-fourth the radius of the earth. Use the result of Problem 2 to predictthe ratio gmoon/gearth. In reality, gmoon/gearthis roughly one-sixth. How might you explain anydiscrepancy between the predicted and actual ratio?Problem 4 Minimum powerIn the readings we estimated the flight speed that minimizes energy consumption. Call that speedvE. We could also have estimated vP, the speed that minimizes power consumption. What is theratio vP/vE?±or. . .6.055J/2.038J (Spring 2010)Homework 4Do the following problems. Submit your answers and explanations online by 10pm on Wednesday, 10 Mar2010.Open universe: Collaboration, notes, and other sources of information are encouraged. However, avoidlooking up answers to the problem, or to subproblems, until you solve the problem or have tried hard. Thispolicy helps you learn the most from the problems.Homework is graded with a light touch: P (made a decent effort), D (made an indecent effort), or F (did notmake an effort).Problem 1 BandwidthTo keep your divide-and-conquer muscles strong, here is an exercise from lecture: Estimate thebandwidth of a 747 crossing the Atlantic filled with CDROMs.10±bits/s or 10. . .bits/sProblem 2 Gravity versus radiusAssume that planets are uniform spheres. How does g, the gravitational acceleration at the surface,depend on the planet’s radius R? In other words, what is the exponent n ing ∝ Rn? (1)±or. . .Problem 3 Gravity on the moonThe radius of the moon is one-fourth the radius of the earth. Use the result of Problem 2 to predictthe ratio gmoon/gearth. In reality, gmoon/gearthis roughly one-sixth. How might you explain anydiscrepancy between the predicted and actual ratio?Problem 4 Minimum powerIn the readings we estimated the flight speed that minimizes energy consumption. Call that speedvE. We could also have estimated vP, the speed that minimizes power consumption. What is theratio vP/vE?±or. . .Comments on page 1 1Comments on page 1Here is homework 4 on NB in case you would like to collaborate. It has more problems than the previoushomeworks, but they are a lot shorter (and not divided into warmup versus problems). Have fun!With or without a case? This will be much smaller if each CD is in a CD case.I’m assuming he wants the same calculations as class...so no case!It’s a weight issue anyway, not volumewhat stays constant? the planet’s mass or its density? (or something else?)Uniform spheres= constant densityA uniform sphere does have constant density (i.e. density at each point is not a function of its coordinates)but I don’t think that it necessarily mean that each sphere has the same density as each other sphere.Doing Problem 3, however, suggests that we are in fact assuming the same density across all planets vs.same mass.The first statement in this question sounds very factual, making the second one sound very contradictory.Maybe you could start off with saying "Imagine the radius of the moon is..."Could someone give me a hint how to set this up? I think I’m still generally confused by proportionalreasoning... I know how to relate P to E in terms of v, but I’m not sure where to go from there.Which day’s notes discuss this. I don’t recall.Homework 4 / 6.055J/2.038J: Art of approximation in science and engineering (Spring 2010) 2Problem 5 Highway vs city drivingHere is a measure of the importance of drag for a car moving at speed v for a distance d:EdragEkinetic∼ρv2Admcarv2.This ratio is equivalent to the ratiomass of the air displacedmass of the carand to the ratioρairρcar×dlcar,where ρcaris the density of the car (its mass divided by its volume) and lcaris the length of the car.Make estimates for a typical car and find the distance d at which the ratio becomes significant (say,roughly 1).10±m or 10. . .mTo include in the explanation box: How does the distance compare with the distance between exitson the highway and between stop signs or stoplights on city streets? What therefore are the mainmechanisms of energy loss in city and in highway driving?Problem 6 MountainsHere are the heights of the tallest mountains on Mars and Earth.Mars 27 km (Mount Olympus)Earth 9 km (Mount Everest)Predict the height of the tallest mountain on Venus.10±km or 10. . .kmTo include in the explanation box: Then check your prediction in a table of astronomical data (or online).Problem 7 Raindrop speedUse the drag-force results from the readings to estimate the terminal speed of a typical raindrop(diameter of about 0.5 cm).10±m s−1or 10. . .m s−1To include in the explanation box: How could you check this result?Homework 4 / 6.055J/2.038J: Art of approximation in science and engineering (Spring 2010) 2Problem 5 Highway vs city drivingHere is a measure of the importance of drag for a car moving at speed v for a distance d:EdragEkinetic∼ρv2Admcarv2.This ratio is equivalent to the ratiomass of the air displacedmass of the carand to the ratioρairρcar×dlcar,where ρcaris the density of the car (its mass divided by its volume) and lcaris the length of the car.Make estimates for a typical car and find the distance d at which the ratio becomes significant (say,roughly 1).10±m or 10. . .mTo include in the explanation box: How does the distance compare with the distance between exitson the highway and between stop signs or stoplights on city streets? What therefore are the mainmechanisms of energy loss in city and in highway driving?Problem 6 MountainsHere are the heights of the tallest mountains on Mars and