Relative Motion

Boat A travels east at a speed of $v_A = 30$ km/h. Boat B travels due north at a speed of $v_B = 45$ km/h.

A river current flows from west to east at 3.0 m/s. A boat is heading in a direction 30° east of north with a speed of 2.0 m/s relative to the water.

Consider a ferry with a speed of 20 m/s in still water, crossing a 600 m wide river. The speed of the river current is 17.32 m/s (as found in the previous problem).

Car A starts at position $x_{A0}$ with a constant velocity $v_A$. Car B starts at the origin with an initial velocity $v_{B0}$ and a constant negative acceleration $a_B$. Assume $v_{B0} > v_A > 0$ and $x_{A0} > 0$.

A rigid ring with radius $R$ undergoes pure rolling on a rigid horizontal surface. The center of the ring moves forward horizontally with a constant velocity $v_0$. Consider a point P on the ring that is at the same height as the center.

Particle A moves along the line $y=d$ with a constant velocity $\vec{v}$ of magnitude $v$ parallel to the x-axis. At the instant particle A passes the y-axis, particle B leaves the origin with zero initial speed and a constant acceleration $\vec{a}$ of magnitude $a$. The angle $\theta$ is between the acceleration vector $\vec{a}$ and the positive direction of the y-axis.

A rabbit runs along a straight line at a constant speed of $v_r = 5$ m/s. At a certain moment, a fox spots the rabbit and begins to chase it. The fox maintains a constant speed of $v_f = 4$ m/s, and its velocity vector at any instant points directly towards the rabbit. The distance between them initially decreases and then increases. The minimum distance between the fox and the rabbit is $d_{min} = 30$ m.

Two ships, A and B, leave port at the same time. Ship A travels northwest at 24 knots, and ship B travels at 28 knots in a direction 40° west of south. (1 knot = 1 nautical mile per hour).

During a calm rain, raindrops fall vertically to the ground with a speed of 10 m/s. A cylindrical measuring container with a cross-sectional area of 80 cm² is placed on the ground. After 30 min, the water level of the collected rainwater in the container is 1 cm high. Now, due to wind, the raindrops fall at an angle of $30^{\circ}$ to the vertical.

A river of width $D$ flows with a constant velocity $\vec{u}$ to the East (positive $x$). A boat launches from the South bank with a speed $v$ relative to the water. The boatman can steer the boat at any angle $\theta$ relative to the line perpendicular to the bank (i.e., $\theta = 0^\circ$ is straight North, $\theta > 0$ is upstream/West).