Question

While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38 degrees with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed of the raindrops relative to the ground. From these observations, determine the angle of the raindrops relative to the ground.

Answer 1

Explanation:

In the velocity triangle in the attachment we have

w = velocity of raindrop relative to ground.

v1 = 25 m/s, velocity of the car (going north) relative to ground.

u1 = velocity of raindrop relative to car

w = vector sum of u1 and v1

v2 = 25 m/s, velocity of the car (going south) relative to ground.

u2 = velocity of raindrop relative to car (vertically down)

w = vector sum of u2 and v2

from the figure we can write

$u_2=\frac{(v_1+v_2)}{tan38} = \frac{50}{tan38}$

= 64.08 m/s

now, we can calculate w as resultant of v2 and u2

w = $\sqrt{25^2+64.08^2}$

w=  68.7 m/s

also, direction of w  theta = arctan(v2/u2) = 21.3 °