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
Staff Emeritus
Homework Helper
587.5 versus 587.2 km/hr. Hmmm. That's a mighty big difference.

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?

SteamKing
Staff Emeritus