How Is the Angle of Displacement Calculated in Vector Travel?

[GingerBread27]

A plane flies 400 km east from city A to city B in 45.0 min and then 940 km south from city B to city C in 1.50 h. (Assume i points east and j points north

In magnitude-angle notation, what is the plane's displacement for the total trip

I figured out the displacement is 1021.57 m but i can't figure out the angle. How is this done.

 

[Sirus]

I think what they mean by "magnitude-angle notation" is simply vector notation, so a magnitude and a direction must be given. Did you draw a picture? The first thing you do in a vector problem is draw a diagram, then it becomes easy. Use trigonometry to find the angle.

 

[GingerBread27]

The answer to the question must be given in m and an angle, so it's not vector notation it's just two numbers straight out. I've tried using trig and keep getting the wrong answer.

 

[Pyrrhus]

show us the trig you've been doing, so we can see where it is wrong...

 

[GingerBread27]

I've done arctan of 940/400, I've done arctan of 940/400 and tried adding and subtracting 180. It's all wrong.

 

[HallsofIvy]

Why are you using 400 and 940? Those are the distances in km the airplane would fly in one hour[\b]. The problem tells you that the airplane flies east at 400 km/h for only 45 minutes (what distance does it cover?) and flies south at 940 km/h for 1 1/2 hours (what distance does it cover?).

 

[GingerBread27]

the 400 and 940 are only displacements, they aren't velocities. I thought you found the angle of displacement by using those numbers.

 

[HallsofIvy]

the 400 and 940 are only displacements, they aren't velocities. I thought you found the angle of displacement by using those numbers.

Ah, sorry, you are right. You don't really need the time then- I thought they were speeds.

Okay, If you draw a picture taking θ as the angle "east of south", you have a right triangle with "opposite side" has length 400 km and the "near side" has length 940 km. tan(θ)= 400/940= 0.4225 and so θ= 23 degrees.

Now! How are you writing the angle? As I said, that is 23 degrees "east of south". You could also give it as "67 degrees south of east" (90- 23= 67) or, measured clockwise from north as on a compass, as 157 degrees (180- 23= 157).