Relative Velocity

Relative Velocity

• objects move within a medium which is moving with respect to an observer

• an airplane encounters wind• a motor boat moves in a river with a current

The magnitude of the velocity (speed) of the moving object with respect to the observer on land will not be the same as the speedometer reading of the vehicle.

Motion is relative to the observer.

The observer on land, often named (or misnamed) the "stationary observer" would measure the speed to be different than that of the person on the boat.

The observed speed of the boat must always be described relative to something.

I’m standing on the back of a pickup truck (that is motionless), throwing apples forwards…

I can throw an apple at exactly 15 m/s. If a friend were standing on the sidewalk,

how fast would she say the apples are moving?

She sees them exactly the same way as me, she will say 15 m/s.

• The truck starts to move forward at 25 m/s.

• I’m still throwing apples forward.

• I’m not paying attention to the truck moving.

• How fast would I say apples are moving?

• Still 15 m/s relative to me.

• How fast does my friend see the apples moving?

• 25 + 15 = 40 m/s

• Think about you driving in a car or flying in a plane and throwing something forward.

• Now I turn around and start throwing the apples out the back of the truck.

• I would still say the apples are moving at 15 m/s, because from my point of view, that’s how fast they’re moving.

• My friend on the sidewalk says the apples are moving at…

• 25 + -15 = 10 m/s

• What if the truck was moving forward at 15 m/s and I was throwing apples out the back of the truck at 15 m/s.

• Myth Busters

You might have even noticed relative velocity while sitting at a red light…Have you ever been sitting at a red light with a bus stopped next to you?You’re kind of daydreaming, looking out the window at the side of the bus, when all of a sudden it feels like your car is rolling backwards!Then you realize that it was just the bus moving forwards.Your brain knows that the bus was just sitting there on the road…it became part of the frame of reference of the ground.When your brain saw the bus moving forwards, it had already “decided” that the bus won’t move. The only option remaining is that you must be moving backwards.

As shown in the diagram below, the plane travels with a resulting velocity of 125 km/hr relative to the ground.

Side Winds

Now consider a plane traveling with a velocity of 100 km/hr [South] which encounters a side wind of 25 km/hr [West]. Now what would the resulting velocity of the plane be?

The resulting velocity of the plane is the vector sum of the two individual velocities.

To determine the resultant velocity, the plane velocity (relative to the air) must be added to the wind velocity.

Can find the direction with trig.

The Boat and the River

The effect of the wind upon the plane is similar to the effect of the river current upon the motor boat. If a motor boat 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.

Example 1 A motor boat traveling 4.0 m/s east encounters a

current traveling 3.0 m/s south.

1.What is the resultant velocity of the motor boat?

2.If the width of the river is 60 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?

Riverboat Simulator

Example 2A motor boat can travel at 4.0 m/s in calm water. The boat wants to head directly east across a river that has a current of 3.0 m/s south.

1.What does the heading of the boat need to be?

2.How much time does it take the boat to travel shore to shore?

Riverboat Simulator