List of Possible Real-World Problems for Exam 1

    One of these problems will be on Exam 1:
     
  1. You are hiking in the mountains with some friends when you come across a deep chasm.  One of your friends wonders if her 150-ft climbing rope is long enough to safely rappel down to the bottom.  She decides to estimate the depth of the chasm by dropping a rock and timing its fall with her stopwatch.  She starts timing as a medium-sized stone is dropped, and when she hears it hit the bottom, she stops the watch, which shows a time of 3.25 seconds.  After carefully analyzing the situation, she decides to attempt the descent.  Was this a wise decision?
  2. In July, 1999 there was a medical emergency involving a research scientist who found a lump in her breast while working at the Amundsen-Scott South Pole Station. The American researcher could not be transported back to a U.S. hospital since no plane could land or take off in the extreme Antarctic winter conditions. The only feasible solution was for a transport plane to fly 14 hours (6,375 miles) round-trip from New Zealand to drop an ultrasound unit and medical supplies near the research camp so the woman could be examined and treated by the on-site physician.  The drop had to be made as close to the research camp as possible since the staff only had about seven minutes to retrieve the important medical package before the staff or fragile supplies suffered from the extreme cold (about 80 degrees below zero!). The flight crew of the U.S. Air Force Starlifter needed to hit a drop zone 3,000 feet long and 400 feet wide as the transport jet flew 200 mph over the frozen polar surface. What instructions would you give to the airplane crew so that they could drop the package as close as possible to the target?  If the package was released 10 seconds too late, would the research staff be able to safely retrieve the precious supplies? Be sure to clearly explain any assumptions you make in solving this problem.Website reference: http://cnn.com/WORLD/asiapcf/9907/11/polar.emergency.03/
  3. A friend of yours is working on a race car and wants to get your expert physics advice.  He reports that the record time for his car to accelerate from rest to the finish line of the quarter-mile dragstrip is 8.23 s.  Your friend is puzzled why his car is not winning more races even though his engine is more powerful than most of the cars in the same racing class.  He is considering spending $10,000 to modify the engine for increased power that he thinks will reduce his race time. What do you recommend?
  4. You and your friend are meeting your parents for dinner at 5:00 pm. It is 4:45 pm and the two of you are 12 blocks away from the restaurant. Your friend wants to take a taxi, but you think you can get there quicker by running. You decide to see who's right. You know that you can run a 7-minute mile. Being a city native you know that taxis are slow during rush hour traffic, but your friend gets into a cab before you can tell her that with slow traffic the taxi will only average about 5 mph. You smile and start running because you know you'll get there first. Are you right? If so how long will you have to wait for your friend to show up?
  5. After a long day, you drive home and park your car in the driveway.  As you walk to the front door, you hear a sound behind you.  When you turn around, you see your car starting to roll back down the driveway - evidently the car popped out of gear and is now coasting down the hill!  Luckily, the driveway is rather long (about 100 feet), but you are currently about that same distance away on the right side of the car.  You estimate that the bottom of the driveway is about 10 feet below the top elevation.  Will you be able to run to the car and apply the brake before the car rolls out into traffic?  (Assume that the car is unlocked and that you will not spend time trying to solve this problem before running to catch the car!)
  6. Jim is riding in bicycle a race that begins in Raleigh at 9:30 am and ends in Chapel Hill, a total distance of 40 miles. On a calm day with no wind, he maintains an average speed of 20 mph. However, on the day of the race, he is riding against the wind of 5 mph. Once Jim reaches Chapel Hill, he needs to walk to his car, which is parked 1/2 mile away from the finish line and get back to Raleigh in order to have lunch with a friend at 1:00 pm. (Assume he does not shower, he goes directly there.) When will Jim arrive in Chapel Hill? At what minimum speed must he drive in order to make his lunch date?
  7. A soccer player is dribbling the ball toward her opponent's goal when she notices a talent scout for a professional team that she wants to play for in the stands. Just then, a defender trips her and the referee awards her a direct free-kick 10 m from the goal line. She really wants to impress the talent scout so she wants to make the shot as high as possible without going over the goal. At what angle should she kick the ball?
  8. A recruiter for college football is looking for a quarterback to play for his school next year.  He is going to offer a scholarship to a quarterback who can throw a 2-lb football at least 40 mph. The quarterback in the game that he is currently watching had a longest throw of 50 yards to a diving receiver with 10 seconds left in the game. Will the recruiter offer this quarterback a scholarship?
  9. You are the technical advisor for a movie that is being filmed in Wilmington.  One action scene in the movie has a stuntman who will jump off a highway overpass onto a semi trailer truck that is traveling at a constant velocity of 50 km/h.  The distance from the bottom of the overpass to the top of the truck is 3 meters. When should the stuntman jump (note: a negative time, like one second before, is not very helpful), and how much room for error is there in timing the jump?
  10. A long jumper is trying to break the world record of 8.5 m set by Carl Lewis.  How fast will he have to run to beat this record?