Finding the Actual Speed and Direction of an Aircraft. A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north. The jet stream is 100 mi/hr in the northeasterly direction. (a) Express the velocity va of the 747 relative to the air and the velocity vw of the jet stream in terms of i and j. (b) Find the velocity of the 747 relative to the ground. (c) Find the actual speed and direction of the 747 relative to the ground.

A. Va: 0i+550j, Vw: 50√2i+50√2j

B. 50√2i+50√2j+550j

C. 624.7mph and N6.5E

Step-by-step explanation:

A. For va, recall that it just has the y (i) component, which is just equal to its velocity.

for vw, there is an angle of 45 degrees, so to find the components do speed*sin (theta)

and speed * cos (theta)

Therefore,

Va: 0i+550j, Vw: 50√2i+50√2j

B. Simply add the I's and j's together to get your answers here, which gives

(0i+550j) + (50√2i+50√2j)

= 0i+50√2i+550j+50√2j

= 50√2i+50√2j+550j

C. Using Pythagoras theorem

a²+b² = c²

c² = (50√2i+50) ² + (50√2j+550j) ²

where a is i and b is j

For the angle, recall that it's just arctan (j/i)

when putting this into the calculator remember not to include the i and j in the arctan. This number should be 83.5 degrees, however this is not your final answer, compass bearings starting from the left in pre-calculus and other math courses, so subtract 83.5 from 90 to find your bearing.

90°-83.5° = 6.5

This gives, 624.7mph and N6.5E