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 and angle of the raindrops relative to the ground?

Answer 1

While returning back in opposite direction driver see that rain drops are falling vertically down

so horizontal speed of rain with respect to driver must be Zero

while moving towards the north direction driver see that the rain drops makes an angle 38 degree with the vertical

$tan\theta = \frac{v_y}{v_x}$

$tan38 = \frac{v_y}{25 + 25}$

$v_y = 39 m/s$

so the speed of rain is

$v = \sqrt{25^2 + 39^2}$

$v = 46.3 m/s$

also the angle is given as

$\theta = tan^{-1}\frac{39}{25}$

$\theta = 57.3 degree$