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Home > PC > Chapter 10 > Lesson 10.1.2 > Problem 10-25

10-25.

A boat is headed up a river at an angle of with a rate of feet per second. The current is heading down stream at a rate of feet per second. The river is feet wide.

  1. Express the velocity of the boat as a vector in component form without including the effect of the river.

    Right triangle, horizontal leg labeled x, vertical leg labeled y, hypotenuse is ray pointing up & right, labeled 20, angle opposite vertical leg labeled, alpha = 25 degrees.

  2. The actual motion of the boat is the combination of the motion of the boat and the current in the river. Find the vector that gives the actual motion of the boat.

    Use vector addition to find the resultant vector.

    2 rays, first labeled 20 runs right & up, at end of that ray, second ray runs down, labeled negative 5 J.

  3. How long will it take the boat to cross the river?

    Consider the 'i' component of the resultant vector from part (b).

  4. How far up river will the boat arrive?

    Consider the 'j' component of the resultant vector from part (b). Multiply this by the number of seconds found in part (c).

    feet

Irregular area contains angle, labeled 25 degrees, top ray labeled 20 feet per second, points up & right, bottom ray is horizontal segment, & area also contains ray labeled 5 feet per second, pointing down.