Rain is falling vertically with a speed of 35 m s^-1. Winds starts blowing after sometime with

step 1 In this question it is told that rain is falling vertically with a speed of 35 meter per second

Rain is falling vertically with a speed of 35 m s^-1....

Rain is falling vertically with a speed of $35 \mathrm{~m} \mathrm{~s}^{-1}$. Winds starts blowing after sometime with a speed of $12 \mathrm{~m} \mathrm{~s}^{-1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain? (a) $\sin ^{-1}\left(\frac{12}{35}\right)$ (b) $\cos ^{-1}\left(\frac{12}{35}\right)$ (c) $\tan ^{-1}\left(\frac{12}{35}\right)$ (d) $\cot ^{-1}\left(\frac{12}{35}\right)$

Rain is falling vertically with a speed of $35 \mathrm{~m} \mathrm{~s}^{-1}$. Winds starts blowing after sometime with a speed of $12 \mathrm{~m} \mathrm{~s}^{-1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?
(a) $\sin ^{-1}\left(\frac{12}{35}\right)$
(b) $\cos ^{-1}\left(\frac{12}{35}\right)$
(c) $\tan ^{-1}\left(\frac{12}{35}\right)$
(d) $\cot ^{-1}\left(\frac{12}{35}\right)$

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Key Concepts

Relative Velocity

This concept refers to the velocity of an object as observed from a particular frame of reference. It involves subtracting the observer's velocity from the object's velocity to obtain the relative motion. In cases like rain and wind, the apparent direction of the rain is determined by combining the actual velocity of the rain with the wind's velocity relative to the observer.

Vector Composition

Vector composition is the process of breaking a vector into its horizontal and vertical components and then recombining them to analyze the overall effect. This is crucial when dealing with multi-directional forces or motions, as it allows one to understand and calculate the resultant vector, which represents the true magnitude and direction of a combination of effects.

Trigonometric Ratios in Physics

Trigonometric ratios, such as the tangent, sine, and cosine functions, are used to relate the angles and sides of angles in right triangles. In problems involving relative motion, the tangent function can be used to determine the angle between the resultant velocity vector and the vertical by taking the ratio of the horizontal component to the vertical component.

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