Note:

The number 5 m/s as velocity is not correct if we look at it mathematically. If relative velocity and actual velocity are the same, then the problem is not correct. Hence, we will assume the problem to be as follows:

Rain water to a cyclist moving at a speed of 5m/s appears to fall at velocity 4m/s. Find the direction and the actual speed of rain water.

vector v_r = u j

vector v_c= 5 i

Relative velocity of rain with respect to cyclist is given as 4 m/s  = v_r – v_c

Magnitude of the rain velocity needs to be calculated from the expression = sqrt (u² + 5² ) = = 4 m/s

Squaring on both sides, u² + 25 = 16 and hence u = 3 = V_c, the speed of the rain

Direction of observer = tan θ = v_c / v_r = 5/ 3 = -1/(3)^1/2