Question

A jet airliner moving initially at 858 mph

(with respect to the ground) to the east moves

into a region where the wind is blowing at

777 mph in a direction 38◦

north of east.

What is the new speed of the aircraft with

respect to the ground?​

Answer 1

1546.1 mph

Step-by-step explanation:

Let's take the east direction as positive x-direction and north as positive y-direction.

The components of the initial velocity of the jet are:

`v_x = 858 mph\\v_y = 0`

while the components of the wind's velocity are

`a_x = (777)(cos 38^(\circ))=612.2 mph\\a_y = (777)(sin 38^(\circ))=478.4 mph`

So, the components of the new velocity of the jet are:

`v'_x = v_x + a_x = 858+612.2 =1470.2 mph\\v'_y = v_y+a_y = 0+478.4=478.4 mph`

And therefore, the new speed is the magnitude of the new velocity, so:

`v'=√(v'_x^2+v'_y^2 )=√((1470.2)^2+(478.4)^2)=1546.1 mph`