Multiple choice

Tom heads directly across a river at a speed of 10 km/hr in his boat. The river is flowing at a speed of 6 km/hr. Find the measure of the angle of resultant path of boat with the shoreline.

  1. 200

  2. 400

  3. 590

  4. 700
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The boat velocity vector is (10, 6) relative to the shore. The angle theta with the shoreline is tan(theta) = 10 / 6 = 1.666. theta = arctan(1.666) = 59 degrees.

AI explanation

The boat heads directly across at 10 km/hr while the river flows downstream at 6 km/hr. The angle of the resultant path with the shoreline is found using the tangent function, where the tangent of the angle equals the boat speed divided by the river speed, yielding tan(theta) = 10/6. Using the arctangent function gives an angle of approximately 59 degrees.

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