Question

A surfer is moving at a constant velocity of 5.2 m/s north relative to a wave which is pushing him west at a constant velocity of 8.6 m/s toward the beach. The surfer begins at a distance of 41 meters away from the beach. How far north does the surfer make it (in meters) before becoming beached? Round answer to 1 decimal place.

Answer 1

The speed and distances are directly proportional. Use ratios to solve for vertical y-distance. The ratio of x-distance west to y-distance north equals the x-velocity to y-velocity.

x/y = vx/vy
41/y = 8.6/5.2
41/y = 1.65
41/1.65 = y
24.8 m = y