Question

wind is blowing at constant velocity v towards west. a man initially at rest starts moving with constant acceleration a towards north then the moment of time at which direction of winds appears south west to him

Answer 1

Answer:

Let v makes angle ‘A’ with horizontal. when man feels that wind is blowing in east then component of wind’s velocity is 0 w.r.t man i.e. vsinA – at=0 t=vsinA/a nw A= 45 bcoz sinA  1 and A can’t be 90 as initially velocity was in north-east direction

Answer 2

The moment at which the direction of wind appears southwest to him is at |V| /a second.

Given:

The wind is blowing towards the west with constant velocity V.

To Find:

The moment at which the direction of wind appears southwest to the man

Solution:

From the figure ,

In ΔWOR

Cosθ = |V| / |R|

⇒ |R| Cosθ = |V|

At θ= 45°

⇒ |R| Cos45° = |V|

⇒ |R|/√2 = |V| ----------------(1)

Sinθ = |V0| / |R|

⇒ |R| Sinθ = |V0|

At θ= 45°

⇒ |R| Sin45° = |V0|

⇒ |R|/√2 = |V0| --------------(2)

From Equation (1) and Equation (2)

|V| = |V0|

From Equation of motions

v = u + at

u = 0 , v = |V|

⇒ |V| = at

⇒ t = |V| / a

∴ The moment of time at which direction of wind appears south west to the man is at  |V|/a  second.

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