Question 1

A person walks inside a train at $$1.2\ \mathrm{m/s}$$ relative to the train. The train moves at $$15.0\ \mathrm{m/s}$$ relative to the ground in the same direction as the person. What is the velocity of the person relative to the ground?

Accepted Answer

$$16.2\ \mathrm{m/s}$$

Question 2

If the person in the previous question walks in the opposite direction to the train's motion at $$1.2\ \mathrm{m/s}$$, what is the person's velocity relative to the ground?

Accepted Answer

$$13.8\ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the velocity of object 1 relative to object 3 in terms of other relative velocities?

Accepted Answer

$$\vec{v}_{13} = \vec{v}_{12} + \vec{v}_{23}$$

Question 4

A person climbs a vertical ladder at $$0.24\ \mathrm{m/s} on a $$train moving at $$0.68\ \mathrm{m/s}$$ horizontally. What is the magnitude of the person's velocity relative to the ground?

Accepted Answer

$$0.72\ \mathrm{m/s}$$

Question 5

What is the direction (relative to the horizontal) of the person's velocity in the previous question?

Accepted Answer

$$19^\circ$$ above the horizontal

Question 6

A boat moves at $$6.1\ \mathrm{m/s}$$ relative to the water, pointing $$25^\circ$$ upstream. The river flows at $$1.4\ \mathrm{m/s}. $$What is the $$x-$$component of the boat's velocity relative to the ground?

Accepted Answer

$$5.5\ \mathrm{m/s}$$

Question 7

For the same boat, what is the $$y-$$component of the boat's velocity relative to the ground?

Accepted Answer

$$1.2\ \mathrm{m/s}$$

Question 8

If the boat wants to move straight across the river (perpendicular to the shore), what angle should it point upstream?

Accepted Answer

$$13^\circ$$

Question 9

Suppose the boat must move directly across the river at $$5.0\ \mathrm{m/s}$$ relative to the ground. The river flows at $$1.4\ \mathrm{m/s}. $$What is the required speed of the boat relative to the water?

Accepted Answer

$$5.2\ \mathrm{m/s}$$

Question 10

What is the direction (relative to the $$x-$$axis) of the boat's velocity relative to the water in the previous question?

Accepted Answer

$$16^\circ$$

Question 11

Which of the following statements about relative velocity is correct?

Accepted Answer

$$\vec{v}_{ba} = -\vec{v}_{ab}$$

Question 12

A swimmer can swim at $$2.0\ \mathrm{m/s} in $$still water. If the river flows at $$1.0\ \mathrm{m/s}$$, what is the swimmer's speed relative to the ground if she swims directly across the river?

Accepted Answer

$$2.2\ \mathrm{m/s}$$

Question 13

A pilot wants to fly due north at $$200\ \mathrm{km/h}$$ relative to the ground. If the wind blows from the west at $$50\ \mathrm{km/h}$$, what should be the magnitude of the plane's velocity relative to the air?

Accepted Answer

$$206\ \mathrm{km/h}$$

Question 14

Which of the following best describes the process for finding the velocity of an object relative to the ground when it is moving within another moving object?

Accepted Answer

Add the velocity of the object relative to the moving object to the velocity of the moving object relative to the ground.

Relative Motion and Vector Addition in Physics

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