4. 2D Kinematics

Sam is driving down the road at $30\mathrm{m}/\mathrm{s}$. Toni, who is in front of Sam, is driving $25\mathrm{m}/\mathrm{s}$ in the same direction. Toni, watching in her rear-view mirror, sees Sam reach out the window and throw a ball towards her. If Sam sees the ball moving away from him at $10\mathrm{m}/\mathrm{s}$, does Toni see the ball moving towards her, or away from her? How fast is the ball moving according to Toni?

On still water, Olive can paddle her kayak $5\mathrm{m}/\mathrm{s}$. She wishes to cross a river which flows east at $2\mathrm{m}/\mathrm{s}$. If Olive is standing on the south bank, and would like to reach a point directly across the river on the north bank, at what angle upstream (west of north) should she point her Kayak?

A railroad flatcar is traveling to the right at a speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. E3.30). What is the velocity (magnitude and direction) of the scooter relative to the flatcar if the scooter's velocity relative to the observer on the ground is (a) 18.0 m/s to the right?

Two piers, A and B, are located on a river; B is 1500 m downstream from A (Fig. E3.32). Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The velocity of the river is 2.80 km/h in the direction from A to B. How much time does it take each person to make the round trip?

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

A 'moving sidewalk' in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks (b) In the opposite direction?

A 'moving sidewalk' in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks (a) in the same direction the sidewalk is moving?

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. (b) How much time is required to cross the river?

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. (a) What is your velocity (magnitude and direction) relative to the earth?

A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to 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. (a) 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 m/s. The plane is in a 10–m/s wind blowing toward the southwest relative to the earth. (b) Let x be east and y be north, and find the components of υ→ P/E.

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