2-D Motion HW #1 P3.6. Prepare: The position vector d whose magnitude d is 10 m has an x-component of 6 m. It makes an angle with the +x-axis in the first quadrant. We will use trigonometric relations to find the y-component of the position vector. Solve: Using trigonometry, dx = d cos , or 6 m = (10 m) cos . This gives 53.1 . Thus the y-component of the position vector d is dy = d sin (10 m) sin 53.1 = 8 m. Assess: The y-component is positive since the position vector is in the first quadrant. P3.8. Prepare: The figure below shows the components vx and vy, and the angle . We will use Tactics Box 3.3 to find the sign attached to the components of a vector. Solve: (a) Since vx v cos , we have 2.5 m/s (3.0 m/s) cos cos 1 (2.5 m/s 30 m/s) 33.6 34 . (b) The vertical component is v y v sin (3.0 m/s) sin 33.6 1.7 m/s.