Coordinate Systems conversion/Component Vectors
1. The polar coordinates of a point are \( r=5.50 \mathrm{~m} \) and \( \theta=240^{\circ} \). What are the Cartesian coordinates of this point?
2. Obtain expressions in component form for the position vectors having the following polar coordinates: (a) \( 12.8 \mathrm{~m}, 150^{\circ} \) (b) \( 3.30 \mathrm{~cm}, 60.0^{\circ} \) (c) \( 22.0 \) in., \( 215^{\circ} \)
3. Solve for the resultant of \( \vec{A}=2.5 \mathrm{~N}, 16.0^{\circ} \mathrm{N} \) of \( \mathrm{E} \), and \( \overrightarrow{\mathrm{B}}=10.0 \mathrm{~N}, 40^{\circ} \mathrm{E} \) of \( \mathrm{N} \) using component method.
4. Solve for the resultant of \( \vec{A}=3.0 \mathrm{~N}, 150 \circ, \vec{B}=2.0 \mathrm{~N}, 100^{\circ} \) and \( \overrightarrow{\mathrm{c}}=1.0 \mathrm{~N}, 50^{\circ} \) using component method.
5. Solve for the resultant of \( \vec{A}=35.0 \mathrm{~N}, 15.0 \circ, \overrightarrow{\mathrm{B}}=20.0 \mathrm{~N}, 45 \circ \mathrm{W} \) of \( \mathrm{N} \) and \( \overrightarrow{\mathrm{c}}=25.0 \) N, \( 30^{\circ} \mathrm{E} \) of \( \mathrm{N} \) using component method.
