Sample Vector Problems

1. Find the x and y components of the following vectors:

a. 240 N at 330º
b. 34 m/s at 210º
c. 15 m at 12º
d. 20 m/s² at 90º

2. From the x and y components given, find the direction and magnitude of the resultant.

a. F_y = 120 N, F_x = 345 N
b. v_y = 31 m/s, v_x = 8 m/s
c. a_x = -15 m/s², a_y = 12 m/s²

3. Add the three vectors below. Use the graphical method to show a picture of the addition of the vectors. Use the mathematical method to obtain the magnitude and direction of the resultant vector.
A = 450 N at 20º, B = 25 N at 270º, C = 230 N at 70º

4. A soccerball is kicked with a horizontal velocity of 11.3 m/s and a vertical velocity of 3.5 m/s. What is the magnitude and direction of the ball's velocity?

5. A shot putter applies a force of 415 N to a shot at an angle of 37º. What are the horizontal and vertical components of this force?