A car travels due east with a speed of $50.0 \mathrm{~km} / \mathrm{h}$. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of $60.0^{\circ}$ with the vertical. Find the velocity of the rain with respect to (a) the car

Find the sum of these four vector forces: $12.0 \mathrm{~N}$ to the right at $35.0^{\circ}$ above the horizontal, $31.0 \mathrm{~N}$ to the left at $55.0^{\circ}$ above the horizontal, $8.40 \mathrm{~N}$ to the left at $35.0^{\circ}$ below the horizontal, and $24.0 \mathrm{~N}$ to the right at $55.0^{\circ}$ below the horizontal. (Hint $\mid \mathrm{N}$ stands for newton, the SI unit of force. The component method allows the addition of any vectors-forces as well as displacements and velocities. Make a drawing of this situation, and select the best axes for $x$ and $y$ so that you have the least number of components.)

A particle undergoes two displacements. The first has a magnitude of $150 \mathrm{~cm}$ and makes an angle of $120.0^{\circ}$ with the positive $x$-axis. The resultant of the two displacements is $140 \mathrm{~cm}$, directed at an angle of $35.0^{\circ}$ to the positive $x$-axis. Find the magnitude and direction of the second displacement.

A science student is riding on a flatcar of a train traveling along a straight horizontal track at a constant speed of $10.0 \mathrm{~m} / \mathrm{s}$. The student throws a ball along a path that she judges to make an initial angle of $60.0^{\circ}$ with the horizontal and to be in line with the track. The student's professor, who is standing on the ground nearby, observes the ball to rise vertically. How high does the ball rise?

Two vectors have unequal magnitudes. Can their sum be zero? Explain.