Question

A political party has to start its procession in an area where wind is blowing at a speed of

30 \sqrt{2} km h^{- 1}

and party flags on the cars are fluttering along north-east direction. If the procession starts with a speed of

40 km h^{- 1}

towards north, find the direction of flags on the cars.

Accepted Answer

When the procession is stationary, the flags flutter along the north-east direction. It means wind is flowing along the north-east direction. The flags will start fluttering along the direction of the relative velocity of wind with respect to procession.

${\vec{v}}_{wc} = {\vec{v}}_{w} - {\vec{v}}_{c}$ $= (30 \sqrt{2} \cos 45 ° \hat{i} + 30 \sqrt{2} \sin 45 ° \hat{j}) - 40 \hat{j} = (30 \hat{i} - 10 \hat{j}) {m s}^{- 1}$

Here the direction of the relative velocity of the wind is $tanθ = \frac{|{\vec{v}}_{c}|}{|{\vec{v}}_{w}| \cos (45 °)} = \frac{40}{30 \sqrt{2} (\frac{1}{\sqrt{2}})} = \frac{4}{3}$

So, the flag will flutter in a direction at $θ = \tan^{- 1} (4 / 3)$ in south-east direction.

B M Sharma Solutions for Chapter: Kinematics II, Exercise 51: ILLUSTRATION 5.47

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Kinematics II, Exercise 51: ILLUSTRATION 5.47

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