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An aeroplane pilot wishes to fly due wes...

An aeroplane pilot wishes to fly due west A wind of `100 km h^-1` is blowing towards south.
(a) If the speed of the plane (its speed in still air) is `300 km h^-1` in which direction should the pilot head ?
(b) What is the speed of the plane with respect tom ground ? Illustrate with a vector diagram.

Text Solution

Verified by Experts

Velocity of air (wind) `= v_A = 100 km h^-1`
Velocity of plane w.r.t. air `= v_(P//A) = 300 km h^-1`
`vec v_P = vec v_(P//A) + vec v_A`
The net velocity of the plane will be the vector sum of two velocities.
Velocity of air and velocity of plane is to move towards west finally, then the N - S component of velocity should be zero. For this,
`v_(P//A) sin theta = v_A`
`rArr 300 sin theta = 100`
`rArr sin theta = (1)/(3) rArr theta = sin^-1 ((1)/(3))`
So the pilot should head in direction `theta = sin^-1 ((1)/(3)) N of W`.
Speed of plane w.r.t ground,
`v_P = v_(P//A) cos theta`
=`300 sqrt(1 - sin^2 theta) = 300 sqrt(1 - ((1)/(3))^2) = 200 sqrt(2) km h^-1`
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