Physics kinetics circular motion

Question

Two velocity vectors, one of 38 m/s at 154 degrees to the origin and one of 21 m/s at 35 degrees to the origin are added. Compute their sum two ways; one graphically (a sketch), and one analytically (with numbers).

Answer 1

For the graphical method, use graph paper an draw the two vectors to scale. Do this by assigning a value to the squares on the paper. If you draw each vector starting at the origin, then the sum is found by drawing parallel lines to form a parallelogram. There are 2 diagonals--the one starting at the origin is the vector sum.

For the analytical solution. find the x and y components of each vector, add them to get the x and y components of the vector sum, and then convert back to the polar form.

The x component is the magnitude times the cosine of the angle, and--for y--use the sine of the angle.

Once you have the combined x and y values, use the Pythagorean Theorem to find the magnitude, and the trig formulas to find the angle.