A student was riding his bicycle from north to south at a speed of 5 m/s when it started to rain. If the rain was falling vertically downward with a velocity of 10 m/s, in which direction should he hold his umbrella?

double the distance = divide strength by 4

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west