4. 2D Kinematics

Intro to Relative Velocity

4. 2D Kinematics

Intro to Relative Velocity

Guided videos.

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?

Has a video solution.

Multiple Choice

Sam is driving down the road at

30 m / s

. Toni, who is in front of Sam, is driving

25 m / 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 m / s

, does Toni see the ball moving towards her, or away from her? How fast is the ball moving according to Toni?

167

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Multiple Choice

On still water, Olive can paddle her kayak

5 m / s

. She wishes to cross a river which flows east at

2 m / 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?

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Textbook Question

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?

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Textbook Question

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.

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Textbook Question

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?

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Textbook Question

153

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Textbook Question

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?

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rank

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Textbook Question

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?

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Textbook Question

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.

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Textbook Question

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?

1096

views

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Textbook Question

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.

174

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Textbook Question

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

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Textbook Question

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

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Textbook Question

(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?

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Textbook Question

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?

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Textbook Question

A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s. (b) How long will it take him to cross?

870

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Textbook Question

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. b. What is the speed of ship A as seen by ship B?

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Textbook Question

While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

226

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Textbook Question

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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Textbook Question

(II) Two cars approach a street corner at right angles to each other (Fig. 3–57). Car 1 travels at a speed relative to Earth v₁ₑ = 35 km/h, and car 2 at v₂ₑ = 55 km/h . What is the relative velocity of car 1 as seen by car 2? What is the velocity of car 2 relative to car 1?

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Textbook Question

(II) Raindrops make an angle θ with the vertical when viewed through a moving train window (Fig. 3–55). If the speed of the train is vₜ , what is the speed of the raindrops in the reference frame of the Earth in which they are assumed to fall vertically?

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Textbook Question

(II) (a) At what upstream angle must the swimmer in Problem 71 aim, if she is to arrive at a point directly across the stream? (b) How long will it take her?

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Textbook Question

(II) An airplane is heading due south at a speed of 688 km/h. If a wind begins blowing from the southwest at a speed of 85.0 km/h (average), calculate

(a) the velocity (magnitude and direction) of the plane, relative to the ground, and . [Hint: First draw a diagram.]

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Textbook Question

(II) A motorboat whose speed in still water is 4.30 m/s must aim upstream at an angle of 23.5° (with respect to a line perpendicular to the shore) in order to travel directly across the stream.

(b) What is the resultant speed of the boat with respect to the shore? (See Fig. 3–33.)

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Intro to Relative Velocity

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