Relative Velocity

To solve the problem of finding the relationship between the angles and when rain is pouring at angle and a woman runs against it making angle with the vertical, we need to consider both the horizontal and vertical components of the velocities involved.

The rain's velocity can be decomposed into horizontal and vertical components as follows:

• Horizontal component:
• Vertical component:

The woman's velocity is purely horizontal.

From the woman's perspective, the rain appears to fall at an angle with the vertical. The effective horizontal and vertical velocities as seen by the woman are:

• Effective horizontal velocity:
• Effective vertical velocity:

The angle with the vertical can be determined using the tangent function, which is the ratio of the effective horizontal velocity to the effective vertical velocity:

Thus, the correct relationship is: