vectors and mass

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dopey9

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Jul 14, 2006
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A particle of mass m kg is acted on by two forces F1 and F2 with magnitudes 3root5 newtons and root5 newtons ad drections parallel to the vectors i+2j and i-2j respectively

The particle is initially at a position given by vector 2i+j

iv calculated the cartesian components of F1 and F2
F1 = 3i+6j
F2 = i 2j

iv also calculated the cartesian component of the total force F1+F2 = (3i+6j)+(i-2j) = 4i +4j

however the part im struggling on is that now the particle is of mass 1kg and is initially at rest, i have to use newtons 2nd law to write down an equation of motion and find the position of the particle after 1second.

so far iv tried:
F=ma
F1+F2= 1a
therefore a = 4i+4j but then i dont know how to find the new posistion ...can anyonehelp thankz
 
I'm assuming the forces are constant ... you have not indicated that they are variable.

the key here is to work in one direction at a time since motion in each direction is independent of the other.

recap the forces ... F1 = 3i + 6j, F2 = i - 2j

in the x-direction ...
initial position = 2i
net force = 4i
a = F/m = 4i/1 = 4i
since x<sub>f</sub> = x<sub>o</sub> + v<sub>0</sub>t + (1/2)at<sup>2</sup> ...
x<sub>f</sub> = 2i + (1/2)(4i)(1<sup>2</sup>) = 4i

can you complete the problem in the y-direction?
 
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