1. Relative Velocity

2. How are observations that are made in different reference frames related to each other?
Relative Velocity

3. What speed does the observer see each of the trains moving at?

4. What speed does an observer on the express train see the local train moving at?

5. When the velocities are along the same line, we can just add or subtract to find the relative velocity.

6. We need to use vector addition to find relative velocity.
First, we need to sketch and label the situation.
Second, we need to label each velocity with subscripts that identify the object and the reference frame
Relative Velocity

7. Veg=velocity of express train relative to the ground
Reference frame
In which velocity
applies
Veg
Veg=velocity of express train relative to the ground
Veg= 60mph N
Vlg=35mph N
Note: Vlg = -Vgl
object

8. Relative to express
Vle
Vle= Vlg + Vge
Notice that inner subscripts (rhs) are the same. Outer subscripts (rhs) are the same as subscripts on lhs.
Vle= 35mph +(-60mph)
Vle=-25mph
local

9. Vle Vle= Vlg + Vge Vle= -35mph +(-60mph) Relative to express local

10. Vel Vel= Veg + Vgl Vel= 60mph +(35mph) Relative to local express

11. The engine of boat drives it across a river that is 1800m wide
The engine of boat drives it across a river that is 1800m wide. The velocity of the boat relative to the water is 4.0m/s, directed perpendicular to the current. The velocity of the water relative to the shore is 2.0m/s.
A) What is the velocity of the boat relative to the shore?
Vbw = velocity of the boat relative to the water
Vws = velocity of the water relative to the shore
Find vbs = velocity of boat relative to shore

12. vbs vbw vws A) What is the velocity of the boat relative to the shore?
Vbw = 4.0 m/s
Vws = 2.0 m/s
vbs = vbw + vws = 4.5 m/s (using the pythagorean theorem)
tanƟ = vbw / vws so Ɵ=63°

13. vab=vag+vgb Vag=25m/s Vbg=15.8m/s
Two cars are approaching an intersection along perpendicular roads. The cars have velocities as shown in the figure.
A) What is the velocity of car A as measured by a passenger in car B.
vab=vag+vgb
Vag=25m/s A
Vbg=15.8m/s B

14. Homework: p. 84 #54, 55, 56, 57, 60, 61