4. 2D Kinematics

Ships A and B leave port together. For the next two hours, ship A travels at 20 mph in a direction 30° west of north while ship B travels 20° east of north at 25 mph. What is the speed of ship A as seen by ship B?

(II) In what direction should the pilot aim the plane in Problem 67 so that it will fly due south?

A person going for a morning jog on the deck of a cruise ship is running toward the bow (front) of the ship at 2.5 m/s while the ship is moving ahead at 8.8 m/s. What is the velocity of the jogger relative to the water? Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now? 

(II) A swimmer is capable of swimming 0.60 m/s in still water. (a) If she aims her body directly across a 55-m-wide river whose current is 0.50 m/s, how far downstream (from a point opposite her starting point) will she land? (b) How long will it take her to reach the other side? 

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.

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?

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 child, who is 45 m from the bank of a river, is being carried helplessly downstream by the river's swift current of 1.0 m/s . As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line (Fig. 3–67) until she reaches the child at a point downstream. If the lifeguard can swim at a speed of 2.0 m/s relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child?

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A boat on a river is traveling from a pier to a point 500 m upstream (against the river's current). The current flows at 4 m/s. If the boat makes the trip in 250 s, what is the speed of the boat relative to the water?

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?

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 in the same direction the sidewalk is moving?

Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent's speed relative to Susan's reference frame?