Resultant of 2 forces physics problem...?

Question

Two forces are applied to a car in an effort to accelerate it.

Please let me know how to actually figure out this answer since I am doing it incorrectly. I dont need the solution but I need to know what to do...

A car is driving straight up.
The first force is 10 degrees to the West of the vertical line that goes through this car. (450N)
The second force is 30 degrees to the East of this vertical line (380N)

What si the resultant of these two forces?

Answer 1

Sorry, I missed your specification of the forces --- it was late at night! I'm withdrawing my original response.

But I hope that you'll take the following comments in the spirit they're intended, to help improve communication. (Sorry, as a lifelong educator, I just can't help myself!)

It would be clearer to write:

"The direction of the first force (450N) is 10 degrees to the West of North."

That way most closely associates the 450N with "force," and clarifies your ambiguous "straight up."

In fact, I also didn't KNOW initially what you meant by "A car is driving straight up." NOT vertically, surely! I thought you might mean "straight up a hill of some given slope"! (If the car were on the flat, your question would presumably be being asked in two dimensions. But if there's a hill, this could bring in three dimensional considerations --- you'd have to specify more carefully whether these forces were horizontal, or parallel to the hill, or ...)

It now seems, only much later, that what you meant by "straight up" was "due North"!

I hope these confusions of mine, from reading your text, will encourage you to try to express yourself more clearly and accurately. After all, when you're writing for others, the aim is presumably good communication.

Good luck with that in future; meanwhile, I commend the approach immediately below to you.

Live long and prosper.

Answer 2

Resolve the 450 N and 380 forces along the North (up).

Along North they are 450 cos 10 & 380 cos 10 (North is adjacent to this angle) N.

Adding the two (450 + 380) cos 10 = 817. 39 N in the North direction

The other component of 450N is 450 sin 10 and is in the direction of West = 78.14 N
The other component of 380N is 380 sin 10 and is in the direction of East = 65.99 N.

The resultant of these two is along the greater force
= (78.14 - 65.99) or (450 -380) sin10 = 12.15 along West.

The resultant of 723.23 and 12.15 is found by square root of the sum of the squares of these two.

R = 723.33 N.

The angle is found using tan a = 12.5(West) / 723.23 (North).

a = 1 degree from the North toward west. {From the Denominator to the Numerator)