Question

The velocity of the current in a river is C = 0.6i + 0.8j km/hr. A boat moves relative to the water with velocity v=7i km/hr. a. What is the speed of the boat relative to the riverbed? b. What angle does the velocity of the boat relative to the riverbed make with the vector v? c. What does the angle from part b tell us in practical terms?

Answer 1

Answer:

  a. 7.64 km/h

  b. 6.0°

  c. see below

Step-by-step explanation:

a) The total velocity of the boat is ...

  7i +(0.6i +0.8j) = 7.6i +0.8j

The magnitude of this velocity is the speed of the boat, relative to land. That is given by the Pythagorean theorem.

  |7.6i +0.8j| = √(7.6² +0.8²) = √58.4 ≈ 7.642 . . . . km/h

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b) The angle of the total velocity with respect to the "i" direction (the direction of vector v) is ...

  α = arctan(0.8/7.6) ≈ 6.009°

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c) The boat is headed in a direction 6° different from its velocity relative to the water. That may need to be accounted for if the boat is traveling any significant distance.