Calculating Net Force on a Solar Sailplane Traveling from Earth to Mars

[ally1h]

Homework Statement

A solar sailplane is going from Earth to Mars. Its sail is oriented to give a solar radiation of 8.00x10^2 N. The gravitational force due to the Sun is 173 N. And the gravitational force due to Earth is 1.00x10^2 N. All forces are in the lane formed by Earth, Sun, and sailplane. The mass of the sailplane is 14,500 kg. What is the net force (magnitude and direction) acting on the sailplane?

<img src="http://farm4.static.flickr.com/3070/2630742185_01c6dba522.jpg?v=0">
(I guess I can't use HTML here... the illustration can be found at the link above)

Homework Equations

Pythagorean theorem

The Attempt at a Solution

I posted this problem once before. Solved it beautifully with the help provided at this forum. Except, when my teacher assigned this problem he forgot to give us the illustration to go along with it and told the class to do it over.

I tried various trig functions and tried adding them together. I don't think I'm doing it correctly, however. This is what I have:
x = 800cos(30) = 692.82
y = 800sin(30) = 400
x+y= 1092.82

x = 173cos(90) = 0
y = 173sin(90) = 173
x+y = 173

x = 100cos(90) = 0
y = 100sin(90) = 90
x+y = 90Sum of all forces = 1092.82 + (-173) + (-90) = 829.82 N

 

[nicksauce]

It looks okay, except for the second force. The angle should be 0, not 90. Also to get the magnitude of the net force, you should add all the x components together and y components together from all the forces first, then find the magnitude.

 

[ally1h]

Okay. Can you tell me why the angle should be 0?

So, if the second force the angle is 0 then
x = 173cos(0) = 173, and
y = 173 sin(0) = 0then adding all 3 forces together its
sum of all x = 692.82 + (-173) + 0 = 519.82 N
sum of all y = 400 + 0 + (-90) = 310

From there do I do the Pythagorean theorem to get the magnitude?
(519.82)^2 + (310)^2 = 366312.8
take the square root of 366312.8 = 605.24

And to get the direction, use the inverse tan function?
tan of angle -1= 310/519.82 = 30.8 degrees?
which that really just checks the work. So for direction I suppose I say 'towards Mars'?