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 10.00 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 = 10.00 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 = 11.18 km/hr –θ = tan -1 (5.00 km/hr /10.00 km/hr) –θ = 26.6° east of north