In this worksheet, we will practice calculating the motion of objects relative to each other using the Galilean transformation.

**Q1: **

A man standing still at a train station watches a train move past him eastwards at 20 m/s. Two boys inside the train throw a baseball. The ball is thrown westwards, at a speed of 5.0 m/s relative to the boy that throws the ball. What is the velocity of the ball as measured by the man in the train station? Assume that eastwards corresponds to positive values of displacement.

- A 23 m/s
- B 25 m/s
- C 20 m/s
- D 15 m/s
- E 17 m/s

**Q3: **

The velocity of a particle in reference frame is m/s. The velocity of reference frame with respect to reference frame is and the velocity of reference frame with respect to is . What is the velocity of the particle in reference frame ?

- A
- B
- C
- D
- E

**Q4: **

A seagull can fly at a velocity of 9.00 m/s in still air.

If it takes the bird seconds to travel 6.00 km straight into an oncoming wind, what is the velocity of the wind?

If the bird turns around and flies with the wind, how long will it take the bird to return 6.00 km?

**Q5: **

A lorry is travelling eastwards at 80 km/h. At an intersection 32 km east of the lorry’s position, a car is travelling north at 50 km/h. At an instant , after the car passes the intersection, the vehicles have positions which are less distant from each other than are any other positions that the vehicles subsequently have.

How much time elapses between the car passing the intersection and the instant ?

- A 880 s
- B 870 s
- C 910 s
- D 900 s
- E 930 s

What is the distance between the vehicles at the instant ?

- A 17 km
- B 20 km
- C 15 km
- D 11 km
- E 22 km

**Q6: **

Two speedboats, boat A and boat B, are traveling in opposite directions to each other along a flowing river, moving toward and away from the flow direction respectively. If the river was not flowing, then the boats would move at the same speed as each other. An observer on the riverbank sees boat A move at 6.0 m/s and boat B move at 7.5 m/s.

What is the speed of boat A relative to the river’s flow?

What is the speed of boat B relative to the river’s flow?

The river’s banks are parallel to the river. What is the speed of the river’s flow relative its banks?

**Q7: **

A boat can be rowed at 8.0 km/h in still water.

How much time is required to row 1.50 km downstream in a river moving 3.0 km/h relative to the shore?

How much time is required for the return trip?

In what direction must the boat be aimed to row straight across the river?

Suppose the river is 0.80 km wide. How much time is required for the boat to get to the opposite shore?

Suppose the river is 0.80 km wide and the boat is aimed straight across the river. How much time is required to get to the opposite shore?

**Q8: **

A boat heads north in still water at 4.5 m/s directly across a river that is running east at 3.0 m/s.

What is the speed of the boat with respect to a point on the riverbed?

At what angle north of east does the boat move with respect to a point on the riverbed?

**Q9: **

A river flows parallel to its banks, eastwards, at 3.2 m/s. A boat starts out from a dock on a bank of the river, heading north of west at 5.8 m/s. The river is m wide.

What is the magnitude of the velocity of the boat with respect to Earth?

- A 6.3 m/s
- B 2.1 m/s
- C 8.4 m/s
- D 4.2 m/s
- E 12 m/s

How much time does it take the boat to reach the opposite bank of the river?

- A 380 s
- B 320 s
- C 270 s
- D 180 s
- E 440 s

**Q10: **

Raindrops fall vertically at 4.5 m/s relative to the earth. An observer in a car moves through the rain at 17.9 m/s in a straight-line. The observer measures the velocity of the raindrops relative to the car.

What speed does the observer measure the raindrops to move at?

At what angle below the horizontal does the observer measure as the direction of the raindrops’ velocity?

**Q11: **

A flight attendant pushes a cart down the aisle of a plane in flight. In determining the acceleration of the cart relative to the plane, which factor do you not need to consider?

- AThe force with which the flight attendant’s feet push on the floor
- BThe friction of the cart’s wheels
- CThe mass of the items in the cart
- DThe velocity of the plane
- EThe mass of the plane

**Q12: **

A parachutist’s fall to Earth is determined by two opposing forces. A gravitational force of 539 N acts on the parachutist. After 2.00 s, she opens her parachute and experiences a force due to air resistance of 615 N. At what speed is the parachutist falling after 10.0 s?

**Q13: **

Near the end of a marathon, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s and the second a velocity of 4.20 m/s. The front runner is 250 m away from the finish line.

What is the velocity of the second runner relative to the first?

Who will win the race, assuming they run at a constant velocity?

- Athe second runner
- Bthe first runner

What distance ahead will the winner be when she crosses the finish line?

- A 6.71 m
- B 4.71 m
- C 4.17 m
- D 3.89 m
- E 2.65 m

**Q14: **

A pilot must fly his plane due north to reach his destination. At full power, the plane can fly at 300 km/h in still air. A wind is blowing southwest at 90 km/h and the plane is flying at full power.

What is the speed of the plane relative to the ground?

- A 220 km/h
- B 210 km/h
- C 260 km/h
- D 240 km/h
- E 270 km/h

At what angle east of north must the plane be directed to fly due north?

**Q15: **

A truck is traveling south at a speed of 70.0 km/h toward an intersection. A car is traveling east toward the intersection at a speed of 80.0 km/h, as shown in the diagram.

What is the magnitude of the velocity of the car relative to the truck?

At what angle north of east is the velocity of the car relative to the truck?

**Q16: **

A man is running on a straight road that makes an angle of with a train track. The man is running away from the track at a speed of 15.0 m/s. A train is moving at a speed of 40.0 m/s with respect to the track. What is the speed of the man with respect to a passenger sitting on the train?

- A 55.0 m/s
- B 25.0 m/s
- C 15.0 m/s
- D 31.2 m/s
- E 40.0 m/s

**Q17: **

On a certain space–time diagram, time is shown on the diagram’s vertical axis.

Which of the following describes how the world line of an object that remains at rest at a specific position would be displayed on the diagram?

- AA vertical line shifted to the right
- BA horizontal line coinciding with the position axis
- CA parabola
- DA vertical line coinciding with the time axis
- EAn inclined line making an angle of with the time axis

Which of the following describes how the world line of an object that moves at a constant velocity would be displayed on the diagram?

- AAn inclined line making an angle of with the time axis
- BA horizontal line
- CA straight line with an angle of with the time axis
- DA parabola
- EA vertical line

Which of the following describes how the world line of an object that begins at rest and accelerates at a constant rate would be displayed on the diagram?

- AAn inclined line with an angle of to the position axis
- BA parabola symmetric about the positive time axis
- CA parabola symmetric about the positive position axis
- DA parabola symmetric about the negative position axis
- EA parabola symmetric about the negative time axis

**Q18: **

When observed from the Sun at a particular instant, Mercury and Venus appear to be moving in opposite directions with speeds km/h and km/h respectively. What is the speed of Mercury at this instant when observed from Venus?