When you are running 8m/sec due east then flag flutter in North and if you run 2m/sec due south flag flutter in North East direction.find velocity of wind by assuming wind velocity uniform in both cases?

Question

Answer

Problem Statement: Find the velocity of the wind by assuming uniform wind velocity in both cases when you are running 8m/sec due east then flag flutter in North and if you run 2m/sec due south flag flutter in North East direction.

Given:

Velocity of the runner due east = 8 m/s

Velocity of the runner due south = 2 m/s

Direction of fluttering of the flag = North and North East

Assumption:

Wind velocity is uniform in both cases

Solution:

Let the velocity of the wind be 'v' and the direction of the wind be 'θ'.

When the flag flutters in the north direction, it means that the wind is blowing from north to south.

Therefore, the velocity of the wind in the north-south direction is 'v'.

Here, the runner is running due east, i.e., perpendicular to the direction of the wind.

Hence, the only component of the wind velocity that affects the runner is the north-south component.

Therefore, the velocity of the runner due to the wind in the north-south direction is also 'v'.

Thus, the net velocity of the runner in the north-south direction is (8 - v) m/s.

When the flag flutters in the north-east direction, it means that the wind is blowing from the north-west direction.

Therefore, the velocity of the wind in the north-south direction is still 'v', but the velocity of the wind in the east-west direction is also 'v'.

Here, the runner is running due south, i.e., perpendicular to the east-west direction of the wind.

Hence, the only component of the wind velocity that affects the runner is the north-south component.

Therefore, the velocity of the runner due to the wind in the north-south direction is still 'v'.

Thus, the net velocity of the runner in the north-south direction is (2 + v) m/s.

Also, the net velocity of the runner in the east-west direction is (8 - v) m/s.

Now, we can use trigonometry to find the magnitude and direction of the wind velocity v:

From the first case, we have (8 - v)^2 + v^2 = w^2, where 'w' is the magnitude of the wind velocity.

From the second case, we have (2 + v)^2 + (8 - v)^2 = w^2, where 'w' is the magnitude of the wind velocity.

Solving these two equations, we get v = 3 m/s and w = 6 m/s.

Therefore

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