Add forces as vectors help - Thanks

[nukeman]

Homework Statement

I am not understanding this. This is the question, and the correct solutions for the question I need help with.

I really don't understand how to get the answer here! Can anyone help me? First steps?

Question:

Answer:

Homework Equations

The Attempt at a Solution

 

[technician]

Are you confident with the idea that you have 2 forces which are vectors.
In the first case the vectors (20N and 15N) are at 90 degrees. To find acceleration you divide F by m (5kg) giving 2 acceleration vectors 4 and 3 at 90 degrees.
You need to find the resultant of these 2 perpendicular vectors (pythagoras !)
In the second case the logic is the same but the angle is not 90 degrees.
Is this any help?

 

[nukeman]

I understand how to get (4i + 3j) but how did they eventually come up with 5 m/s^2 at 36.9 degreeS?

 

[DrewD]

The magnitude of the vector comes from the pythagorean theorem by treating the two vectors as perpendicular sides of a triangle. Trig is the best way to get the angle. How's your trig?