A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. How much time is required to cross the river?

An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. What is the speed of the plane over the ground? Draw a vector diagram.

An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. If the airspeed of the plane (its speed in still air) is 320.0 km/h (about 200 mi/h), in which direction should the pilot head?

The nose of an ultralight plane is pointed due south, and its airspeed indicator shows $35\text{ m/s}$. The plane is in a $10\text{ m/s}$ wind blowing toward the southwest relative to the earth. Let $x$ be east and $y$ be north, and find the components of ${\overrightarrow{v}}_{P/E}$ .

The nose of an ultralight plane is pointed due south, and its airspeed indicator shows $35\(\text{ m/s}\)$. The plane is in a $10\(\text{ m/s}\)$ wind blowing toward the southwest relative to the earth. In a vector-addition diagram, show the relationship of $\(\overrightarrow{v}\)_{P/E}$ (the velocity of the plane relative to the earth) to the two given vectors.

A river flows due south with a speed of 2.0 m/s. You steer a motorboat across the river; your velocity relative to the water is 4.2 m/s due east. The river is 500 m wide. What is your velocity (magnitude and direction) relative to the earth?