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Chapter 2: Problem 116

A horizontal wind is blowing with a velocity \(v\) towards north-east. A man starts running towards north with acceleration \(a\). The time, after which man will feel the wind blowing towards east, is (A) \(\frac{v}{a}\) (B) \(\frac{\sqrt{2} v}{a}\) (C) \(\frac{v}{\sqrt{2} a}\) (D) \(\frac{2 v}{a}\)

Short Answer

Expert verified
The short answer is (A) \(\frac{v}{a}\).

Step by step solution

01

1. Wind and man's velocity components

First, let's determine the components of the wind's velocity. Since it's blowing towards the north-east, its components will be equal towards north and east: \(v_n = v\) \(v_e = v\) Now, let's determine the components of the man's velocity. Initially, he is running towards the north with acceleration \(a\), so: \(v_mn = at\) \(v_me = 0\) (since he is not running eastwards initially)
02

2. Relative velocity components

Next, let's find the components of the relative velocity between the man and the wind. We have to subtract the man's velocity components from the wind's components: \(v_rn = v_n - v_mn = v - at\) \(v_re = v_e - v_me = v\)
03

3. Condition for the wind blowing towards east

The man will feel the wind blowing towards east when the relative velocity in the north has the same magnitude as the relative velocity in the east: \(v_rn = v_re\)
04

4. Solve for time

Using the equation from step 3, we can solve for the time \(t\): \(v - at = v\) \(at = v\) \(t = \frac{v}{a}\) Therefore, the correct answer is (A) \(\frac{v}{a}\).

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