1.
The waterfall is 3 km away in a direction [latex]15°[/latex] south of west.
Chapter 9: Vectors
Suggested Homework Problems
For Problems 1–6, sketch a vector to represent the quantity.
The waterfall is 3 km away in a direction [latex]15°[/latex] south of west.
The cave entrance is 450 meters away, [latex]45°[/latex] north of east.
The current is moving 6 feet per second in a direction [latex]60°[/latex] east of north.
The bird is flying due south at 45 miles per hour.
The projectile was launched at a speed of 40 meters per second at an angle of [latex]30°[/latex] above horizontal.
The baseball was hit straight up at a speed of 60 miles per hour.
For Problems 7–10, which vectors are equal?
For Problems 11–14, sketch a vector equal to [latex]\bf{v}\text{,}[/latex] but starting at the given point.
[latex](4,-1)[/latex]
[latex](-3,1)[/latex]
[latex](0,-2)[/latex]
[latex](-3,-1)[/latex]
For Problems 15–18, draw the scalar multiples of the given vectors.
[latex]-2\bf{v}[/latex] and [latex]1.5\bf{v}[/latex]
[latex]\dfrac{-1}{2}\bf{w}[/latex] and [latex]3\bf{w}[/latex]
[latex]-2.5\bf{u}[/latex] and [latex]\sqrt{2}\bf{u}[/latex]
[latex]-\sqrt{6}\bf{t}[/latex] and [latex]5.4\bf{t}[/latex]
For Problems 19–26,
[latex]\bf{A} = \bf{u} + \bf{v}[/latex]
[latex]\bf{B} = \bf{z} + \bf{u}[/latex]
[latex]\bf{C} = \bf{w} + \bf{u}[/latex]
[latex]\bf{D} = \bf{G} + \bf{z}[/latex]
[latex]\bf{E} = \bf{z} + \bf{F}[/latex]
[latex]\bf{F} = \bf{w} + \bf{v}[/latex]
[latex]\bf{G} = \bf{w} + \bf{w}[/latex]
[latex]\bf{H} = \bf{G} + \bf{G}[/latex]
For Problems 27–30, find the magnitude and direction of the vector.
[latex]v_x = 5,~ v_y = -12[/latex]
[latex]v_x = -8,~ v_y = 15[/latex]
[latex]v_x = -6,~ v_y = -7[/latex]
[latex]v_x = 1,~ v_y = -3[/latex]
For Problems 31–38, sketch the vectors, then calculate the resultant.
Add the vector [latex]\bf{v}[/latex] of length 45 pointing [latex]26°[/latex] east of north to the vector [latex]\bf{w}[/latex] of length 32 pointing [latex]17°[/latex] south of west.
Add the vector [latex]\bf{v}[/latex] of length 105 pointing [latex]41°[/latex] west of south to the vector [latex]\bf{w}[/latex] of length 77 pointing [latex]8°[/latex] west of north.
Let [latex]\bf{v}[/latex] have length 8 and point in the direction [latex]80°[/latex] counterclockwise from the positive [latex]x[/latex]-axis. Let [latex]\bf{w}[/latex] have length 13 and point in the direction [latex]200°[/latex] counterclockwise from the positive [latex]x[/latex]-axis. Find [latex]\bf{v}+\bf{w}\text{.}[/latex]
Let [latex]\bf{a}[/latex] have length 43 and point in the direction [latex]107°[/latex] counterclockwise from the positive [latex]x[/latex]-axis. Let [latex]\bf{b}[/latex] have length 19 and point in the direction [latex]309°[/latex] counterclockwise from the positive [latex]x[/latex]-axis. Find [latex]\bf{a}+\bf{b}\text{.}[/latex]
Esther swam 3.6 miles heading [latex]20°[/latex] east of north. However, the water current displaced her by 0.9 miles in the direction [latex]37°[/la