Question

(a)

A jet airliner moving initially at 701 mph to the east where there is no wind moves into a region where the wind is blowing at 848 mph in a direction 13◦ north of east.
What is the new speed of the aircraft with respect to the ground? (b)What is the direction of the aircraft (use coun- terclockwise from due East as the positive an- gular direction, between the limits of −180◦ and +180◦)?

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:

vx= 858 mph

vy= 0

while the components of the wind's velocity are

ax= (777)(cos 38)= 612.2 mph

ay= (777)(sin38)= 478.4 mph

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

vx=vx+ax= 858+612.2= 1470.2 mph

vy=vy+ay=0 + 478.4 = 478.4mph

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

v= vx2+vy2= (1470.2)+(478.4)= 1546.1 mph