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Homework Help: Boats - relative velocity

  1. Sep 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Two boat landings are 5.1 km apart on the
    same bank of a streamthat flows at 3.4 km/hr.
    A motorboat makes the round trip between
    the two landings in 1.5 hr.
    What is the speed of the boat relative to
    the water? Answer in units of km/hr.

    2. Relevant equations

    3. The attempt at a solution
    I tried to get the velocity of the water relative to the shore plus the velocity of the boat relative to shore to equal the velocity of the boat relative to the water.

    That would give a right triangle with Vws and Vbs as the legs, and Vbw (what I'm trying to find) as the hypotenuse.

    So I get sqrt ( (5.1 / 0.75)^2 + 3.4^2), which is 7.60 and wrong.

    Please help me, I don't understand what I am doing wrong...
  2. jcsd
  3. Sep 18, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    velocity(boat/shore) = velocity(boat/water) + velocity(water/shore)

    There's no need for any right triangles, since all velocities are in the same (or opposite) direction.

    Hint: Use distance = speed*time
    Set up that equation for when the boat's going upstream and for when its going downstream.
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