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math

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a boat crosses a river and arrives at a point on the opposite bank directly across from its starting position. The boat traveks at 4m/s and the current is 2m/s. If the river is 600 m wide in what direction must the boat steer and how long will it take to cross?

  • math - ,

    current toward -y
    We want to go in +x direction
    steer at angle T up from x axis

    components toward x
    Vx = 4 cos T
    components toward y
    Vy = 4 sin T - 2

    we want Vy = 0
    so
    2 = 4 sin T
    sin T = 1/2
    T = 30 degrees or in compass heading
    30 degrees North of East = 60 degrees true

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