Calc 3: Vector Addition Problem Solution Example

[mikky05v]

I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3.

Homework Statement

Homework Equations

A vector U=<x,y>
||U|| means the length of U = √(x^2 +y^2). vectors can also be written as U = ||U||(cosθi, sinθj)

The Attempt at a Solution

so I start by naming the vectors.V is the direction the plane is now heading. V1 is the original direction of the plane. V2 is the direction of the wind.

V = V1 + V2

V1 = 600(cos148i+sin148j)
V2 = 80(cos45i+sin45j)

next I distributed, combined like terms and factored out i and j
V = (600cos148+80cos45)i + (600sin148+80cos45)j

I plugged that into my calculator and got
V = <-452.7i + 374.5j>

To find the speed I found the length of vector V
||V|| = sqrt[ (-452.7)2+374.52] = 587.5 km/hr

That isn't one of the options.. am i wrong?

 

[SteamKing]

587.5 versus 587.2 km/hr. Hmmm. That's a mighty big difference.

 

[mikky05v]

ya i realize it's extremely close but it is also multiple choice. being "close" to one of 5 possible answers doesn't exactly make me feel confident I am doing it right. Do you have anything helpful to add?

 

[iRaid]

http://www.wolframalpha.com/input/?i=+(600cos148+80cos45)i+++(600sin148+80cos45)j

Your answer is right.

 

[SteamKing]

ya i realize it's extremely close but it is also multiple choice. being "close" to one of 5 possible answers doesn't exactly make me feel confident I am doing it right. Do you have anything helpful to add?

It's rare that you are going to calculate every answer down to the last decimal place.

Would you feel more confident of your approach if NONE of the choices came close to your answer?