Rain falls vertically downward with the velocity of 3.3 m/s. a boy moves at a speed of 5 m/s east in a bicycle with an umbrella. what is the velocity of the rain with respect to the boy?

Refer to the diagram shown below.

The velocity of the rain relative to the boy is given by

in a vectorial sense as shown in the figure.

Given:
Vr = 3.3 m/s
Vb = 5 m/s

Use the Pythagorean to obtain
Vr/b = √(3.3² + 5²) = 6 m/s

The angle that Vr/b makes with due east is
θ = tan⁻¹ (3.3/5) = 33.4°

The velocity of the rain with respect to the boy is 6 m/s.
The direction of the rain is 33.4° north of due east.

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