Relative Velocity

Relative Velocity

​BHS Physics

Dec. 1, 2022

Relative Velocity and River Boat Problems

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Relative Velocity and Riverboat Problems

​Using the information provided at https://www.physicsclassroom.com/class/vectors/Lesson-1/Relative-Velocity-and-Riverboat-Problems, answer the questions that follow.

Multiple Choice

On occasion objects move within a medium that is moving with respect to an observer. For example, an airplane usually encounters a wind - air that is moving with respect to an observer on the ground below. As another example, a motorboat in a river is moving amidst a river current - water that is moving with respect to an observer on dry land. In such instances as this, the magnitude of the velocity of the moving object (whether it be a plane or a boat) with respect to the observer on land will __________ as the speedometer reading of the vehicle.

• not be the same

• be the same

Multiple Choice

Consider a plane flying amidst a tailwind. A tailwind is a wind that approaches the plane from behind, thus increasing its resulting velocity. If the plane is traveling at a velocity of 100 km/hr with respect to the air, and if the wind velocity is 25 km/hr, then what is the velocity of the plane relative to an observer on the ground below?

• 25 km/hr

• 125 km/hr

• 100 km/hr

• 0 km/hr

Multiple Choice

Now onsider a plane flying into a headwind. A headwind is a wind that approaches the plane from the front, thus decreasing its resulting velocity. If the plane is traveling at a velocity of 100 km/hr with respect to the air, and if the wind velocity is 25 km/hr, then what is the velocity of the plane relative to an observer on the ground below?

• 50 km/h

• 75 km/h

• 100 km/h

• 125 km/h

Multiple Choice

Consider a plane traveling with a velocity of 100 km/hr, South that encounters a side wind of 25 km/hr, West. Now what would the resulting velocity of the plane be?

(This question can be answered in the same manner as the previous questions. To determine the resultant velocity, the plane velocity must be added to the wind velocity. Since the two vectors to be added - the southward plane velocity and the westward wind velocity - are at right angles to each other, the Pythagorean theorem can be used.)

• 79.3 km/h

• 91.3 km/h

• 103.1 km/h

• 109.7 km/h

Analysis of a Riverboat's Motion

The effect of the wind upon the plane is similar to the effect of the river current upon the motorboat.

If a motorboat were to head straight across a river (that is, if the boat were to point its bow straight towards the other side), it would not reach the shore directly across from its starting point. The river current influences the motion of the boat and carries it downstream.

The boat may be moving with a velocity of 4 m/s directly across the river, yet the resultant velocity of the boat will be greater than 4 m/s and at an angle in the downstream direction. While the speedometer of the boat may read 4 m/s, its speed with respect to an observer on the shore will be greater than 4 m/s.

Multiple Choice

Suppose that the river was moving with a velocity of 3 m/s, North and the motorboat was moving with a velocity of 4 m/s, East. What would be the resultant velocity of the motorboat (i.e., the velocity relative to an observer on the shore)?

(The resultant velocity of the boat can be determined in the same manner as was done for the plane. Since the boat heads straight across the river and since the current is always directed straight downstream, the two vectors are at right angles to each other. Thus, the Pythagorean theorem can be used to determine the resultant velocity.)

• 3 m/s

• 4 m/s

• 5 m/s

• 6 m/s

Analysis of a Riverboat's Motion

Motorboat problems such as these are typically accompanied by three separate questions:

1. What is the resultant velocity (both magnitude and direction) of the boat?

2. If the width of the river is X meters wide, then how much time does it take the boat to travel shore to shore?

3. What distance downstream does the boat reach the opposite shore?

Multiple Choice

A motorboat traveling 4.0 m/s, East encounters a current traveling 3.0 m/s, North.

What is the resultant velocity of the motorboat?

• 3.5 m/s

• 4.0 m/s

• 4.5 m/s

• 5.0 m/s

Multiple Choice

A motorboat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North.

If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?

(time = distance/speed)

• 20 s

• 40 s

• 80 s

• 160 s

Multiple Choice

A motorboat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North.

If the width of the river is 80 meters wide, what distance downstream does the boat reach the opposite shore?

(distance = speed x time)

• 40 m

• 60 m

• 80 m

• 100 m

Multiple Choice

A motorboat traveling 4 m/s, East encounters a current traveling 7 m/s, North.

What is the resultant velocity of the motorboat?

• 4 m/s

• 6 m/s

• 8 m/s

• 10 m/s

Multiple Choice

A motorboat traveling 4 m/s, East encounters a current traveling 7.0 m/s, North.

If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?

• 20 s

• 40 s

• 60 s

• 80 s

Multiple Choice

A motorboat traveling 4 m/s, East encounters a current traveling 7.0 m/s, North.

If the width of the river is 80 meters wide, what distance downstream does the boat reach the opposite shore?

• 80 m

• 100 m

• 120 m

• 140 m

Multiple Choice

A plane travels with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a 10 mi/hr headwind.

• 70 mph

• 80 mph

• 90 mph

• 100 mph

Multiple Choice

A plane travels with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a 10 mi/hr tailwind.

• 70 mph

• 80 mph

• 90 mph

• 100 mph

Multiple Choice

A plane travels with a speed of 80 mi/hr with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a 60 mi/hr crosswind (side wind).

• 70 mph

• 80 mph

• 90 mph

• 100 mph

Multiple Choice

A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, North.

What is the resultant velocity of the motor boat?

• 5.9 m/s

• 7.1 m/s

• 9.7 m/s

• 49.7 m/s

Multiple Choice

A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, North.

If the width of the river is 150 meters wide, then how much time does it take the boat to travel shore to shore?

• 10 s

• 15 s

• 20 s

• 25 s

Multiple Choice

A motorboat traveling 6 m/s, East encounters a current traveling 3.8 m/s, North.

If the width of the river is 150 meters wide, then what distance downstream does the boat reach the opposite shore?

• 77 m

• 86 m

• 95 m

• 113 m

Multiple Choice

A plane is traveling with a speed of 125 mph with respect to the air. Determine the resultant velocity of the plane (magnitude only) if it encounters a 45 mph side wind.

• 69 mph

• 99 mph

• 133 mph

• 145 mph