Frames of Reference and Relative Velocities

Frames of Reference Frame of Reference – The stationary background to which an object is compared to tell if it is moving. “With respect to….” *Always the stationary object

The sun rises over the horizon The horizon A bus moves past people standing on the sidewalk People on the sidewalk A passenger on a train sees a ball roll down the aisle Train aisle Two express subway trains traveling at the same speed on parallel tracks whiz past passengers waiting on the platform of a local station Platform A passenger on one of the subway trains looks out the window and sees another train standing still The other train A person standing near a railroad track sees a train pass by, then notices an airplane fly overhead in the same direction as the train, bust at a much faster speed Railroad track/ground A passenger in the airplane looks down and sees the train moving backwards Inside of the airplane

Relative Velocities General Form: V ac = V ab + V bc Opposite subscript means opposite velocities Vxy = - Vyx

Relative Velocity Scenario: Slow Car, Fast Car along a track Subscripts: Vse = Slow Car with respect to Earth Vfe = Fast Car with respect to Earth Vfs = Fast Car with respect to Slow Car

Practice Problem Vse = +80 km/h N Vfe = +90 km/h N Since the slow car is the frame of reference, we treat it as though it is stationary  V = 0 km/hr Subtract 80 km/h from both sides to get Vse = 0 km/h Vfs = 10 km/h *if you were in the slow car, it would appear as though the fast car is only moving 10 km/h

How your book does it… Vse = +80 km/h N Vfe = +90 km/h N We want to know Vfs –Set up equation so that first letter of subscript is “f” and last letter is “s” Start with Vfe but need to end in “s” so we use Ves Know that Ves = - Vse Vfs = Vfe + (- Vse) Vfs = 90 – 80 = 10 km/h

A boat heading north crosses a wide river with a velocity of 10 km/h relative to the water. The river has a uniform velocity of 5 km/h due east. What is the boat’s velocity with respect to an observer on shore Given: Vbw = 10 km/hr N Vwe = 5 km/h E Vbw Vwe Vbw

A passenger at the rear of the train traveling at 15 m/s relative to the Earth throws a baseball with a speed of 15 m/s in the direction opposite the motion of the train. What is the velocity of the baseball relative to the Earth as it leaves the thrower’s hand. A spy runs form the front to the back of an aircraft carrier at a velocity of 3.5 m/s. If the aircraft carrier is moving forward at 18.0 m/s, how fast does the spy appear to be running when viewed by an observer on a nearby stationary submarine A ferry is crossing a river. If the ferry is headed due north with a speed of 2.5 m/s relative to the water and the river’s velocity is 3.0 m/s to the east, what will the boat’s velocity relative to the Earth be? (Remember to include direction when describing the velocity) A pet-store supply truck moves ta 25.0 m/s north along a highway. Inside, a dog moves at 1.75 m/s at an angle of 35.0° east of north. What is the velocity of the dog relative to the road?