physics question

Question

A plane is flying west at 310 m/s with a crosswind blowing south at 85 m/s. What is

the resultant velocity of the plane?

Select one:

a. 321 m/s @ 22° south of west

b. 227 m/s @ 45° south of west

c. 227 m/s @ 22° south of west

d. 321 m/s @ 45° south of west

Answer 1

A plane is flying west at 310 m/s with a crosswind blowing south at 85 m/s. What is

the resultant velocity of the plane?

Select one:

a. 321 m/s @ 22° south of west

b. 227 m/s @ 45° south of west

c. 227 m/s @ 22° south of west

d. 321 m/s @ 45° south ( west

Resultant = (√Vx² +Vy² )

= √ (96100 + 7225 ) =√ ( 103325) = 321.44

Now for direction

tan ß = Vy/ Vx here Vy is southwords

and Vx is westwords

tan ß = 85/310

Answer 2

You can answer this one without any math!

The plane is traveling 310 m/s west, so when you add the crosswind going south, its *total* velocity must be > 310 m/s. This eliminates options b and c.

Since the crosswind is only 85 m/s and the plane is traveling 310 m/s west, we expect it to be going *mostly* west. Therefore the answer must be a--321 m/s @ 22 degrees south of west.