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15 December, 23:12

An airplane flies from San Francisco to Washington DC at an air speed of 800 km/hr. Assume Washington is due east of San Francisco at a distance of 6000 km. Use a Cartesian system of coordinates centered at San Francisco with Washington in the positive x-direction. At cruising altitude, there is a cross wind blowing from north to south of 100 km/hr.

Required:

a. What must be the direction of flight for the plane to actually arrive in Washington?

b. What is the speed in the San Francisco to Washington direction?

c. How long does it take to cover this distance?

d. What is the time difference compared to no crosswind?

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Answers (1)
  1. 16 December, 00:33
    0
    A.) 7.13 degree north east

    B.) 806.23 km/h

    C.) 7.44 hours

    D.) 0.06 hours

    Explanation:

    Assume Washington is due east of San Francisco and Francisco with Washington in the positive x-direction

    Also, the cross wind is blowing from north to south of 100 km/hr in y coordinate direction.

    A.) Using Cartesian system of coordinates, the direction of flight for the plane to actually arrive in Washington can be calculated by using the formula

    Tan Ø = y/x

    Substitute y = 100 km/h and x = 800km/h

    Tan Ø = 100/800

    Tan Ø = 0.125

    Ø = Tan^-1 (0. 125)

    Ø = 7.13 degrees north east.

    Therefore, the direction of flight for the plane to actually arrive in Washington is 7.13 degree north east

    B.) The speed in the San Francisco to Washington direction can be achieved by using pythagorean theorem

    Speed = sqrt (800^2 + 100^2)

    Speed = sqrt (650000)

    Speed = 806.23 km/h

    C.) Let us use the speed formula

    Speed = distance / time

    Substitute the speed and distance into the formula

    806.23 = 6000 / time

    Make Time the subject of formula

    Time = 6000/806.23

    Time = 7.44 hours

    D.) If there is no cross wind,

    Time = 6000/800

    Time = 7.5 hour

    Time difference = 7.5 - 7.44

    Time difference = 0.06 hours
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