Question

An airplane is flying with velocity of 70km\hr in north east direction .The wind is blowing 30km\hr from north to south.What is the resultant displacement of the aeroplane in 4 h

Answer 1

Answer:

The resultant displacement of the airplane in 4 hours is 212.8 km.

Explanation:

The components of the airplane's velocity and wind's velocity are:

Airplane:

$v_{a_{x}} = v_{a}cos(45) = 70 km/h*cos(45) = 49.50 km/h$

$v_{a_{y}} = v_{a}sin(45) = 70 km/hsin(45) = 49.50 km/h$

Wind:

$v_{w_{x}} = 0$

$v_{w_{y}} = v_{w} = -30 km/h$

Now, to know the new velocity of the airplane we to find the result vector:

$v_{x} = v_{a_{x}} + v_{w_{x}} = 49.50 km/h + 0 = 49.50 km/h$

$v_{y} = v_{a_{y}} + v_{w_{y}} = 49.50 km/h - 30 km/h = 19.50 km/h$  

Now, the magnitude of the new speed of the airplane is:

$v_{a} = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{(49.50 km/h)^{2} + (19.50 km/h)^{2}} = 53.20 km/h$

Finally, after 4 hours the resultant displacement of the airplane is:

$x = v*t = 53.20 km/h*4 h = 212.8 km$

Therefore, the resultant displacement of the airplane in 4 hours is 212.8 km.

I hope it helps you!