A 2 kg object is subjected to three forces that give it an acceleration −→a = =(8.00m/s2 )ˆi + (6.00m/s2 )ˆj. If two of the three forces, are −→F1 = (30.0N)ˆi + (16.0N)ˆj and −→F2 = =(12.0N)ˆi + (8.00N)ˆj, find the third force.

The third force  =

Explanation:

Here we note that, the formula for the resultant force is as follows;

Also

∑F = m×a

Where:

= Force components in the x direction

= Force components in the y direction

∑F = Resultant force vector

m = Mass of the object

a = Acceleration vector ob the object =

Therefore, since ∑F = m×a, we have;

Hence from , we have;

That is 30 + 12 + = 16

∴   = 16 - (30 + 12) = -26

Similarly,

Therefore,   = 12 - (16 + 8) = -12

Hence,

The third force,

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