Question

An aeroplane is flying due to North with a velocity of 90km per HR if the wind be blowing from east with a velocity of 15 km per HR find the resultant velocity and direction of the aeroplane.

Answer 1

velocity of aeroplane, v'=90km/hrs due north
velocity of wind,v"=15km/hrs due east
therefore, resultant velocity , r =
$\sqrt{ {90}^{2} + {15}^{2} + 2 \times 90 \times 15 \times \cos(45) } = 101.16 \:km \: per \: hours$
and direction of aeroplane is due northwest

Answer 2

Answer:

The resultant velocity and direction of the airplane is 91.24 km/hr due to east.

Explanation:

Given that,

Velocity of airplane = 90 km/hr

Velocity of wind = 15 km/hr

The resultant velocity

$R=\sqrt{R_{1}^2+R_{2}^2+2R_{1}R_{2}\cos\theta}$

$R=\sqrt{90^2+15^2+2\times90\times15\times\cos90^{0}}$

$R=\sqrt{90^2+15^2+2\times90\times15\times0}$

$R=\sqrt{90^2+15^2}$

$R= 91.24\ km/hr$

The direction of the airplane is

$tan\theta=\dfrac{90}{15}$

$\theta=tan^{-1}6$

$\theta=80.53\ approx\ 81\ due\ to\ east$

Hence, The resultant velocity and direction of the airplane is 91.24 km/hr due to east.