3. Vectors

Vector Composition & Decomposition

Open Question
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.
Open Question
Draw each of the following vectors. Then find its x- and y-components. (a) v = (7.5 m/s, 30 degrees clockwise from the positive y-axis)
Open Question
Draw each of the following vectors. Then find its x- and y-components. (b) = v = (440 m/s, 30 degrees below the positive x-axis)
Open Question
A cannon tilted upward at 30° fires a cannonball with a speed of 100 m/s. What is the component of the cannonball's velocity parallel to the ground?
Open Question
(II) An airplane is traveling 815 km/h in a direction 41.5° west of north (Fig. 3–40).
(a) Find the components of the velocity vector in the northerly and westerly directions.
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Open Question
(II) (a) 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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Open Question
(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,
Open Question
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) Ax = 2.00m, Ay = −1.00 m;
Open Question
Vector A has y-component Ay = +9.60 m. A makes an angle of 32.0° counterclockwise from the +y-axis. (a) What is the x-component of A? (b) What is the magnitude of A?
Open Question
Draw each of the following vectors. Then find its x- and y-components. (c) F = (50.0 N, 36.9 degrees counterclockwise from the positive y-axis)
Open Question
(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.
Open Question
(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,
Open Question
(II) Two vectors, V₁ (→ above V₁) and V₂ (→ above V₂) , add to a resultant Vᵣ (→ above Vᵣ) = V₁ (→ above V₁) + V₂ (→ above V₂). Describe V₁ (→ above V₁) and V₂ (→ above V₂) if

(b) V²ᵣ = V²₁ + V²₂,