Set 5 Problem number 8

• Problem

• Solution

• Generalized Solution

Problem

What vector of magnitude 4.9 must be added to the displacement vector A = < -1.16 meters, 2.9 meters> 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.)

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 < -1.16 meters, 2.9 meters>, results in a vector whose x component is 0.
• Clearly then the x component of the added vector will have to be - -1.16 meters, 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 4.9 meters.

• 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

• (- -1.16 meters) ^ 2+y ^ 2 = ( 4.9 meters) ^ 2, or 1.34  meters ^ 2 + y ^ 2 = 24.01  meters ^ 2.

• We can solve this equation for y to obtain y = `sqrt( 24.01  meters ^ 2 - 1.34 meters ^ 2) = 24.01  meters.

The vector being added therefore has components - -1.16 meters and 24.01 meters, and is represented <--1.16 meters, 24.01 meters>

• The magnitude and angle of this vector are easily found to be 4.9 meters, as required, and 87.23 degrees.