Relative Motion

A river of width $W$ flows due east at a uniform speed $v_w$. A boat with a speed $v_b$ relative to the water leaves the south bank pointed at an angle $\theta$ west of north.

A steamship is sailing due north at a speed of 15 km/h. A person on the ship observes the smoke from the smokestack drifting due east. Later, the ship sails due east at a speed of 24 km/h, and the person observes the smoke drifting due northwest. It is assumed that the wind velocity is constant during both journeys.

As shown in the diagram, a person on a pier of height $h$ above the water pulls a rope attached to a boat at point A. The person pulls the rope, causing it to be reeled in at a constant speed $V$.

A ferry crosses a river that is 600 m wide. The crossing takes 1.0 min and the ferry's resultant path is perpendicular to the river banks. The speed of the ferry in still water is 20 m/s.

A person running due west at a speed of 2.5 m/s feels the wind coming from due north. If they double their speed, they feel the wind coming from the northwest.

An ice skater skates on a circular path of radius $R = 15$ m at a constant speed $v_0 = 7$ m/s. They throw a ball horizontally from a height $h = 1.5$ m, aiming for it to land at the center of the circle.

A person observes rain streaks on a train window. Angles are measured from the vertical.

• When the train is stopped, the streaks are tilted forward at an angle $\theta_0$.
• When the train moves forward at a constant velocity $v_1$, the streaks are tilted backward at an angle $\theta_1$.
• When the train moves at a new constant velocity $v_2$, the streaks are tilted backward at an angle $\theta_2$.

A boat moves along a river in uniform rectilinear motion with speed $v$. A person on the boat throws an object obliquely forward (in the direction of the boat's motion) with speed $v_0$ relative to the boat, where $v_0$ makes an angle $\theta$ with the horizontal.