Chapter 3–4: Relative Motion Physics Coach Kelsoe Pages 102–105

Objectives Describe situations in terms of frame of reference. Solve problems involving relative velocity.

Frames of Reference If you are moving at 80 km/hr north and a car passes you going 90 km/hr, to you the faster car seems to be moving north at 10 km/hr. Someone standing on the side of the road would measure the velocity of the faster car as 90 km/hr toward the north. This simple example demonstrates that velocity measurements depend on the frame of reference of the observer.

Frames of Reference Consider a stunt dummy dropped from a plane. a)When viewed from the plane, the stunt dummy falls straight down. b)When viewed from a stationary position on the ground, the stunt dummy follows a parabolic projectile path.

Relative Velocity When solving relative velocity problems, write down the information in the form of velocities with subscripts. Using our earlier example, we have: –v se = +80 km/hr north (se = slower car with respect to Earth) –v fe = +90 km/hr north (fe = faster car with respect to Earth) –unknown = v fs (fs = fast car with respect to slow) Write an equation for v fs in terms of the other velocities. The subscripts start with f and end with s. The other subscripts start with the letter that ended the preceding velocity: –v fs = v fe + v es

Relative Velocity An observer in the slow car perceives Earth as moving south at a velocity of 80 km/hr while a stationary observer on the ground (Earth) views the car as moving north at a velocity of 80 km/hr. In equation form: –v es = -v se Thus, this problem can be solved as follows: –v fs = v fe + v es = v fe – v se –v fs = (+90 km/hr n) – (+80 km/hr n) = +10 km/hr n A general form of the relative velocity equation is: –v ac = v ab + v bc

Sample Problem Relative Velocity A boat heading north crosses a wide river with a velocity of km/hr relative to the water. The river has a uniform velocity of 5.00 km/hr due east. Determine the boat’s velocity with respect to an observer on shore.

Sample Problem Solution Set up your coordinate system with your givens. –Given: v bw = km/hr due north (velocity of the boat, b, with respect to the water, w) v we = 5.00 km/hr due east (velocity of the water, w, with respect to the Earth, e) –Unknown: v be = ? –Diagram: See diagram v we v bw v be θ

Sample Problem Solution Choose an equation or situation: –v be = v bw + v we –(v be ) 2 = (v bw ) 2 + (v we ) 2 –tan θ = v we /v bw Rearrange the equations to isolate the unknowns: –v be = √ (v bw ) 2 + (v we ) 2 –θ = tan -1 v we /v bw

Sample Problem Solution Substitute the known values into the equations and solve. –v be = √ (10.00 km/hr) 2 + (5.00 km/hr) 2 –v be = km/hr –θ = tan -1 (5.00 km/hr /10.00 km/hr) –θ = 26.6° east of north