Question

8. Vector ? has a magnitude of 35.0 units and points in the direction 325° counterclockwise from the positive x axis. Calculate the x and y components of this vector.

9. A vector has an x component of -25.0 units and a y component of 40.0 units. Find the magnitude and direction of this vector.

10. A force ? 1 of magnitude 6.00 newtons acts on an object at the origin in a direction θ = 30.0° above the positive x axis. A second force ? 2 of magnitude 5.00 newtons acts on the object in the direction of the positive y axis. a. Find graphically the magnitude and direction of the resultant force ? 1 +? 2. (Do this on graph paper or engineering paper. Measure the resultant and the angle it forms.) b. Use the component method to add the vectors. Express the resultant in unit vector notation.

11. Given the vectors ? = 2.00?̂+6.00?̂ and ? ⃗ = 3.00?̂−2.00?̂ a. Sketch the vector sum ? = ? +? ⃗ b. Calculate ? ⃗ ⃗ in terms of unit vectors. Determine the magnitude and direction of ? . c. Do the same with ? ⃗⃗ = ? ⃗ ⃗ −? ⃗⃗ .

Answer 1

We are given that the magnitude of the vector is 35 units and the
direction is 325 degrees counter clockwise from the x axis. From this we
can make some observations, such as the angle is larger then 270 degree
so the vector is in the 4th quadrant. Any vector that is in the 4th
quadrant will have negative component along y axis and positive
component along x axis. We can also view this angle as 35 degree clock
wise from the positive x axis.

• Component along the x axis

           $V_x = V \cos(35^o) = 35 \times 0.819 = 28.67 \text{ Units}$

• Component along the y axis

          $V_y = V \sin(35^o) = 35 \times 0.573 = 20.8 \text{ Units}$