Question

Raindrops are falling through the air with a velocity of 10ft.per sec .If a north wind blows at 12 m.p.h.,find the direction in which the drops appear to fall to a person walking north at 3m.p.h.With what velocity would they hit his umbrella?

Answer 1

The raindrops are falling vertically at 10 ft/sec. The north wind is blowing at 12 mph, which is approximately 17.6 ft/sec. The person is walking north at 3 mph, which is approximately 4.4 ft/sec.

To the person walking, the raindrops appear to be coming from a direction that is the result of the wind speed minus the person's walking speed, which is 17.6 - 4.4 = 13.2 ft/sec.

The overall velocity of the raindrops, as seen by the person, would be the vector sum of the vertical and horizontal velocities.

So, the velocity with which the raindrops would hit the umbrella can be calculated using Pythagoras' theorem: sqrt[(10)^2 + (13.2)^2] = approximately 16.6 ft/sec.

The direction would be the arctangent of the horizontal speed (13.2 ft/sec) divided by the vertical speed (10 ft/sec), which is approximately 52.6 degrees from the vertical.