3. Vectors

Let θ be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: A_x = 2.00m, A_y = −1.00 m

Draw each of the following vectors. Then find its x- and y-components. v = (7.5 m/s, 30 degrees clockwise from the positive y-axis)

Draw each of the following vectors. Then find its x- and y-components. F = (50.0 N, 36.9 degrees counterclockwise from the positive y-axis)

At t = 0, a particle starts from rest at 𝓍 = 0, y = 0 and moves in the xy plane with an acceleration $\vec{a}=(4.0\hat{i}+3.0\hat{j}){\text{m/s}}^2$. Determine the 𝓍 and y components of velocity.

Let C = (3.15 m, 15 degrees above the neagtive x-axis) and D = (25.6, 30 degrees to the right of the negative y-axis). Find the x and y components of each vector.

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). What is the vertical component of her acceleration?

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Two vectors, ${\vec{V}}_1$ and ${\vec{V}}_2$, add to a resultant ${\vec{V}}_R={\vec{V}}_1+{\vec{V}}_2$. Describe ${\vec{V}}_1$ and ${\vec{V}}_2$ if $V_R^2=V_1^2+V_2^2$.

(III) You are given a vector in the xy plane that has a magnitude of 95.0 units and a y component of -60.0 units. (a) What are the two possibilities for its 𝓍 component? (b) Assuming the 𝓍 component is known to be positive, specify the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the - 𝓍 direction. 

Find the magnitude and direction of the vector represented by the following pairs of components: A_x = −8.60 cm, A_y = 5.20 cm

Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25°, and Paul is pulling a large crate up the ramp with a rope that angles 10° above the ramp. If Paul pulls with a force of 550 N, what are the horizontal and vertical components of his force? (Force is measured in newtons, abbreviated N.)

You are fixing the roof of your house when a hammer breaks loose and slides down. The roof makes an angle of 35° with the horizontal, and the hammer is moving at 4.5 m/s when it reaches the edge. What are the horizontal and vertical components of the hammer's velocity just as it leaves the roof?

(II) At t = 0, a particle starts from rest at 𝓍 = 0 , y = 0 and moves in the xy plane with an acceleration a (→ above a) = (4.0 î + 3.0 ĵ ) m/s². Determine

(a) the 𝓍 and y components of velocity,

What are the x- and y-components of the velocity vector shown in FIGURE EX3.20?