Rain is falling vertically with 3 ms^-1 and a man is moving due North with 4 ms^-1. In which d

step 1 In this question we will learn about some basic concept of the vectors. The question is rain is

Rain is falling vertically with 3 ms^-1 and a man is moving...

Rain is falling vertically with $3 \mathrm{~ms}^{-1}$ and a man is moving due North with $4 \mathrm{~ms}^{-1}$. In which direction he should hold the umbrella to protect himself from rains? (A) $37^{\circ}$ North of vertical (B) $37^{\circ}$ South of vertical (C) $53^{\circ}$ North of vertical (D) $53^{\circ}$ South of vertical

Rain is falling vertically with $3 \mathrm{~ms}^{-1}$ and a man is moving due North with $4 \mathrm{~ms}^{-1}$. In which direction he should hold the umbrella to protect himself from rains?
(A) $37^{\circ}$ North of vertical
(B) $37^{\circ}$ South of vertical
(C) $53^{\circ}$ North of vertical
(D) $53^{\circ}$ South of vertical

Key Concepts

Relative Velocity

Relative velocity is the concept used to determine the apparent velocity of one object as observed from another moving object. In problems like rain observed by a moving person, you subtract the person's velocity vector from the rain's velocity vector to find the effective or relative velocity of the rain with respect to the person. This fundamental idea is crucial in understanding how motion is perceived differently in different frames of reference.

Vector Components and Their Addition

Vectors are mathematical objects that have both magnitude and direction. In many physics problems, including analyzing rain and movement, velocities are represented as vectors which can be decomposed into horizontal and vertical components. By adding these components, one can find the resultant vector, which helps in determining the direction and magnitude of the combined effect of different motions.

Trigonometric Analysis in Kinematics

Trigonometry is essential for analyzing the angles formed by vector components in kinematics. When a vector is broken down into its perpendicular components, functions like sine, cosine, and tangent are used to determine the relationships between the components and the overall direction of the vector. This approach is particularly useful when finding the angle at which an object, like an umbrella, should be oriented relative to a given direction.

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