Vectors Word Problem

Question

An outdoorsman needs to kayak with a speed of 5 miles per hour straight across the river. However, the current is flowing perpendicular to this path at a rate of 2 miles per hour. Sketch a vector diagram to show the kayak’s heading (k), the river’s current (), and the desired resultant (r). Determine the direction and speed the outdoorsman should use to stay on course and on time.

Answer 1

river current speed 2 mph

need to go 5 mph perpendicular to the river current

how fast should the kayak go and in what direction??

construct a right triangle, use the pythagorean theorem d^2 = 5^2 +2^2 = 29, d=sqr29

go about 5.4 = sqr29 mph in a direction of arctan2.5 = about 68.2 degrees NNW if he wants to go 5 mph West and river goes 2 mph South