please help with this work

Question

Two aircrafts, A and B, are flying at approximately the same altitude. Aircraft

A is flying west with a velocity VA = 900 km/h, while aircraft B is flying north

with a velocity VB = 600 km/h. Determine the magnitude and direction of the

velocity which A appears to have to a passenger riding in B

Answer 1

Hello Des -

Glad to help!

Draw the velocity vector for plane B: 600 km/hr North

Then, tail-to-tail, draw the velocity vector for plane A: 900 km/hr West

These two vectors form the sides of a right triangle. Draw in the hypotenuse and its length (calculate by the Pythagorean theorem) will represent the speed at which the two planes are moving away from each other.

Vector length = sq.rt. ( 600² + 900² )

The direction of the answer to this question should either be toward the southwest or toward the northeast.

Imagine you are a passenger in plane B: which way do you see plane A moving? Toward the Southwest!

If you're indicating direction by "south of west", then the smallest angle in the right triangle (the one on the left) is the alternate interior angle to the one you want, and therefore equal to it.

Its opposite side has a length of 600 and its adjacent side has a length of 900, so: tangent = 600/900.

Find the angle whose tangent is 2/3 and you'll have the south-of-west angle you're looking for. :-)

Answer 2

Hello Des,

Let us draw a vector diagram

As B is flying due North , it can be made stationary by applying equal velocity vector in South direction

Now ,Same change is to be made on aircraft A

So the vector diagram has 900 km/hr due West and 600 Km/hr due South

Thus the speed of A with respect of B is in South of West

Given as

√ [ (900)² + (600)² ]

For direction, use tanØ = 600/900 = 2/3