[Grade 12 Physics] How can I calculate the net electrostatic force on this sphere?

Question

"A small metal sphere  X  with a negative charge of -2.50 C is 1.20 cm directly to the left of another sphere  Y  with a charge of +3.00 C. A third sphere  Z  with a charge of +4.00 C is 1.20 cm directly below sphere Y. The three spheres are at the vertices of a right angle triangle, with sphere Y at the right angle. Calculate the net elctrostatic force on sphere Y sketching diagrams if necessary."

I sketched a diagram but found out that I don t understand how to solve for this, I did the 2D collisions unit before and I understood the 2D dimensions vectors etc. but for some reason this isn t quite clicking with me. According to the answers, the solution is 8.83*10^14 N at 122 degrees, but I don t know how to get there.

Jim · Accepted Answer

Without describing the point charge formula for force except this: F = (k)(product of charges)/d²
(hopefully U understand how to manipulate this formula in order to find the force between two point charges)
Using UR description of the charge placement and distances.
The force on charge Y will be in two directions.   The force between Y and Z is repulsion and vertical, +y-axis direction, and the force between Y and X is attraction, and in the -x-axis direction.  The size of these two forces U must calculate using the complete formula described above.   
The size of the force between Y and Z will be proportional to (3)(4) = 12 
The size of the force between Y and X will be proportional to (3)(2.5) = 7.5
(this is true because the only thing different in the formula is the size of each charge)
So the angle, Θ,  of the NET force acting on Y can be found as 90° + arctan (7.5/12) = 90°+32° = 122° ANS
(for the NET force size, the size of each of the two right angled forces must be combined - hypotenuse-wise)

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[Grade 12 Physics] How can I calculate the net electrostatic force on this sphere?

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