Question

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?

Answer 1

Refer to the diagram shown below.

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

`\vec{V}_(r/b) = \vec{V}_(r) - \vec{V}_(b)`
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°
Answer:
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.