Question

While driving north at 21 m/s during a rainstorm you notice that the rain makes an angle of 36° 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 and the angle of the raindrops relative to the ground?

Answer 1

Let the velocity of the vehicle be
V₁ = (21, 0)
Let the velocity of a raindrop be
V₂ = (a, b)

When returning, the raindrop is vertical.
Therefore a = 21 m/s

When driving north, a raindrop makes an angle of 36° with the vertical, therefore
tan(36°) = a/b = 21/b
b = 21/tan(36°) = 28.9 m/s

The speed of a raindrop is
√(a² + b²) = √(441 + 835.44) = 35.73 m/s
The angle is 90-36 = 54° with the ground.

Answer: 35.7 m/s at 54° relative to the ground.