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Set 5 Problem number 8
What vector of magnitude 6.09 must be added to A =
< 8.01, -8.73> in order to obtain a vertical vector R? Answer by giving the magnitude
and angle of the vector to be added.
- (Note on notation: <u,v> stands for a vector
whose x component is u and whose y component is v.)
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 <
8.01, -8.73>, results in a vector whose x component is 0.
- Clearly then the x component of the added vector
will have to be - 8.01, since this is the only way to cancel out the x component of the
original vector and end up with x component 0.
The vector being added must have magnitude 6.09.
- 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
- (- 8.01) ^ 2+y ^ 2 = 6.09 ^ 2, or 64.16 + y ^ 2 =
37.08 .
- We can solve this equation for y to obtain y =
`sqrt( 37.08 - 64.16) = 37.08.
The vector being added therefore has components -
8.01 and 37.08, and is represented <- 8.01, 37.08>
- The magnitude and angle of this vector are easily
found to be 6.09, as required, and 102.18 degrees.
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