Problem: What vector of magnitude 10.11 must be added to A = [ 10, 2] in order to obtain a vertical vector R? Answer by giving the magnitude and angle of the vector. (Note: [u,v] stands for a vector whose x component is u and whose y component is v.)
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Solution: If the resultant vector is to be vertical, then its x component will be 0. So we must find a vector which when added to [ 10, 2], results in a vector whose x component is 0. Clearly the x component of the added vector will have to be - 10, since this is the only way to cancel out the x component of the original vector. Now the added vector must have magnitude 10.11. We can use this fact to find its y component. If y stands for the y component of the added vector, the Pythagorean Theorem tells us that the magnitude of the added vector is (- 10 ^ 2)+y ^ 2 = 10.11 ^ 2, or 100 + y ^ 2 = 102.2 . We can solve this equation for y to obtain y = `sqrt( 102.2 - 100) = 1.487. The added vector therefore has components - 10 and 1.487. The magnitude and angle of this vector are easily found to be 10.10 and 8.456.
Generalized Response:
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Figure description: