(A)A runner is jogging at a steady 7.7 km/hr. when the runner is 3.9 km. form the finish line, a bird begins flying from the runner to the finish line at 46.2 km/hr (6 times as fast as the runner). When the bird reaches the finish line, it turns around and flies back to the runner. How far does the bird travel? Even though the bird is a dod, assume that it occupies only one point in space and that it can turn without loss of speed.

(B) After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. the bird repeats the back and forth trips until the runner reaches the finish line. how far does the bird travel from the beginning ( including the distance traveled to the first encounter).

  1. 👍 0
  2. 👎 0
  3. 👁 360
  1. Flight time of bird to finish line, FL, = 3.9/46.2 = .0844 hr.
    Distance runner travels during this time period = .0844(7.7) = .65km.
    Distance from runner to FL = 3.9 - .65 = 3.25km.
    Net closing speed between runner and bird = 7.7 + 46.2 = 53.9Km/hr.
    Time for runner and bird to meet = 3.25/53.9 = .060 hr.
    Distance covered by runner = .060(7.7) = .462km.
    Distance covered by bird to runner = .060(46.2) = 2.785km.
    Total distance traveled by bird up to first runner-bird meeting = 3.9 + 2.785 = 6.685km.

    Remaining distance of runner to FL = 3.9 - .65 - .462 = 2.788km.
    Time of runner to FL = 2.788/7.7 = .362 hr.
    During this time period, the bird flies back and forth between the runner and the FL at the constant speed of 46.2km/hr covering a total distance of 46.2(.362) = 16.728km.

    Therefore, the total distance traveled by the bird from the start = 6.685 + 16.728 = 23.413km.

    I hope I didn't slip a digit or two.

    Your problem brings to mind a golden oldie from the field of recreational mathematics that you might find amusing.

    Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?

    We want to know the total distance that the fly covers, so let's use Distance = Rate * Time to solve the problem. We already know the fly's rate of flight. If we can find the time that the fly spends in the air, we can figure out how far it travels.
    Ignore the fly for a minute, and concentrate on the trains. The first train is traveling at 60 miles/ hour and the second train is going 90 miles/ hour, so they are approaching each other at 60 miles/ hour + 90 miles/ hour = 150 miles/ hour. Now we know the rate at which the trains are closing in on each other and their distance apart (150 miles), so we can find the time until they crash:
    Distance = Rate * Time
    Time = Distance / Rate
    = (150 miles) / (150 miles/ hour)
    = 1 hour.The fly spends the same amount of time traveling as the trains. It goes 120 miles/ hour, so in the one hour the trains take to collide, the fly will go 120 miles.

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig/Pre-Calc...

    Please help me with this. The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s. The change, t, in a runner's performance is modeled by the function shown below: t= 0.0119s^2 - 0.308s

    asked by AbelovedAngel on October 23, 2014
  2. Precalc

    Water is flowing from a major broken water main at the intersection of two streets. The resulting puddle of water is circular and the radius r of the puddle is given by the equation r = 5t feet, where t represents time in seconds

    asked by Zoe Cameron on April 2, 2015
  3. math

    A relay with n laps was run by 4 people. The first runner ran half the laps. The second runner ran half the amount of laps the first runner ran. The third runner ran half the amount of laps the second runner ran. The remaining

    asked by Tomas on November 14, 2013
  4. Physics

    Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 19 minutes. Part A Determine the drag force on the runner during the

    asked by Anonymous on September 27, 2016
  5. Physics

    In a 5.00km race, one runner runs at a steady 11.6km/h and another runs at 15.0km/h. How long does the faster runner have to wait at the finish line to see the slower runner cross?

    asked by Tommy on June 12, 2015
  1. Physics

    Two runners start simultaneously at oppposite ends of a 200.0 m track and run toward each other. Runner A runs at a steady 8.0 m/s and runner B runs at a constant 7.0 m/s. When and where will these runners meet? How do I start

    asked by Sarah on June 3, 2009
  2. physics

    1.Moving with uniform acceleration a body covers 150m during 10sec so thet it covers 24m during the 10th sec .What is the initial velocity and the acceleration of the body. 2.A runner travels 1.5 laps around a circular track of

    asked by srikar on May 19, 2012
  3. Physics

    A runner of mass 51.5 kg starts from rest and accelerates with a constant acceleration of 1.35 m/s2 until she reaches a velocity of 5.7 m/s. She then continues running with this constant velocity. (Take the direction the runner is

    asked by James on May 18, 2012
  4. phyics

    Suppose a runner completes one lap around a 400-m track in a time of 50 s. Calculate the average velocity of the runner. Express your answer in meters per second to the nearest integer.

    asked by shelby on September 12, 2015
  5. Physics

    A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 6.6 km/hr (3 times as fast as the

    asked by Linda on September 3, 2018
  6. Math

    Runner A crosses the starting line of a marathon and runs at an average pace of 5.6 miles per hour. Half an hour later, Runner B crosses the starting line and runs at an average rate of 6.4 miles per hour. If the length of the

    asked by nick on February 12, 2013

You can view more similar questions or ask a new question.