Problem 20
How do you place the heads and tails of two vectors that you want to add?
Problem 21
How do you add vectors using their components?
Problem 24
Diagram Use a sketch to show that two vectors of unequal magnitude cannot add to zero, but that three vectors of unequal magnitude can.
Problem 24
Use a sketch to show that two vectors of unequal magnitude cannot add to zero, but that three vectors of unequal magnitude can.
Problem 25
Graph Vector \(\overrightarrow{\mathbf{A}}\) has a magnitude of \(27 \mathrm{~m}\) and points in a direction \(32^{\circ}\) above the positive \(x\) axis. Vector \(\overrightarrow{\mathbf{B}}\) has a magnitude of \(35 \mathrm{~m}\) and points in a direction \(55^{\circ}\) below the positive \(x\) axis. Sketch the vectors \(\overrightarrow{\mathbf{A}}, \overrightarrow{\mathbf{B}}\), and \(\overrightarrow{\mathbf{C}}=\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\). Estimate the magnitude and the direction angle of \(\overrightarrow{\mathbf{C}}\) from your sketch.
Problem 27
Calculate Vector \(\overrightarrow{\mathbf{A}}\) points in the positive \(y\) direction and has a magnitude of \(12 \mathrm{~m}\). Vector \(\overrightarrow{\mathbf{B}}\) has a magnitude of \(33 \mathrm{~m}\) and points in the negative \(x\) direction. Find the direction and the magnitude of (a) \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\), (b) \(\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}\), and (c) \(\overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}\).
Problem 27
Vector \(\overrightarrow{\mathbf{A}}\) points in the positive \(y\) direction and has a magnitude of \(12 \mathrm{~m}\). Vector \(\overrightarrow{\mathbf{B}}\) has a magnitude of \(33 \mathrm{~m}\) and points in the negative \(x\) direction. Find the direction and the magnitude of \((\mathbf{a}) \overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}\), (b) \(\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}\), and \((\mathbf{c}) \overrightarrow{\mathbf{B}}-\overrightarrow{\mathbf{A}}\)
Problem 29
The pilot of an airplane wants to fly due north, but there is a \(65 \mathrm{~km} / \mathrm{h}\) wind blowing from east to west. In what direction should the pilot head her plane if its speed relative to the air is \(340 \mathrm{~km} / \mathrm{h}\) ? Give your answer in degrees north of east.
Problem 31
If the velocity of object 1 relative to object 2 is \(v_{12}\) and the velocity of object 2 relative to object 3 is \(v_{23}\), what is the velocity of object 1 relative to object 3 ?
Problem 31
Determine If the velocity of object 1 relative to object 2 is \(v_{12}\) and the velocity of object 2 relative to object 3 is \(v_{23}\), what is the velocity of object 1 relative to object 3 ?
