Relative Velocity Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity What is the understood place or perspective where the car and truck’s velocity is understood to be measured? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity What is the understood place or perspective where the car and truck’s velocity is understood to be measured? The car and truck’s velocity is understood to be measured with respect to an observer on the ground Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity The place or perspective where physics quantities such as velocity, displacement, and acceleration are measured is given a special name in physics. What is it called? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity The place or perspective where physics quantities such as velocity, displacement, and acceleration are measured is given a special name in physics. This is called “Frame of Reference” Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity The place or perspective where physics quantities such as velocity, displacement, and acceleration are measured is given a special name in physics. This is called “Frame of Reference” If no frame of reference is mentioned, the understood reference frame is “ground” or ”the earth” Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity What is the symbol for the velocity of car A with respect to (w.r.t.) ground? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] Note: The first subscript denotes the object, and the second subscript denotes the reference frame. Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] What is AvB = ? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = 80.0 -50.0 = 30.0 km/h [E] Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = 80.0 -50.0 = 30.0 km/h [E] What is BvA = ? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = 80.0 -50.0 = 30.0 km/h [E] BvA = 30.0 km/h [W] Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = 80.0 -50.0 = 30.0 km/h [E] BvA = 30.0 km/h [W] What is BvB = ? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = 80.0 -50.0 = 30.0 km/h [E] BvA = 30.0 km/h [W] BvB = 0.0 km/h Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Rule: For one object approaching another object moving in the same direction along a line, the relative speed = the ___________ between the speeds of the objects with respect to the ground frame of reference. Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity Rule: For one object approaching another object moving in the same direction along a line, the relative speed = the difference between the speeds of the objects with respect to the ground frame of reference. Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity General Rules: How is BvA related to AvB = ? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity General Rules: BvA = -AvB Same magnitude opposite direction Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity General Rules: BvA = -AvB Same magnitude opposite direction AvA = ? Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity General Rules: BvA = -AvB Same magnitude opposite direction AvA = 0.0 km/h Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity General Rules: BvA = -AvB Same magnitude opposite direction AvA = 0.0 km/h Note: The above results are true in 1-d, 2-d and 3-d Truck B = 50.0 km/h [E] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = ? Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = 130.0 km/h [E] Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = 130.0 km/h [E] BvA = ? Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = 130.0 km/h [E] BvA = 130.0 km/h [W] Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = 130.0 km/h [E] BvA = 130.0 km/h [W] Rule: For one object approaching another object moving in opposite directions along a line, the relative speed = the ___________ of the speeds of the objects with respect to the ground frame of reference. Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

Relative Velocity: Head-on collision along a line AvB = 130.0 km/h [E] BvA = 130.0 km/h [W] Rule: For one object approaching another object moving in opposite directions along a line, the relative speed = the sum of the speeds of the objects with respect to the ground frame of reference. Truck B = 50.0 km/h [W] Car A = 80.O km/h [E]

General vector equation for Relative velocity Do you know the vector equation relating AvB, Avg, and Bvg ?

General vector equation for Relative velocity AvB = Avg - Bvg Memorize please !

General vector equation for Relative velocity AvB = Avg - Bvg Note: This vector equation works generally in 1-d, 2-d. and 3-d

General vector equation for Relative velocity AvB = Avg - Bvg Note: This vector equation works generally in 1-d, 2-d. and 3-d Check for rear-end approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E]

General vector equation for Relative velocity AvB = Avg - Bvg Note: This vector equation works generally in 1-d, 2-d. and 3-d Check for rear-end approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = Avg - Bvg Use integers to sub AvB = ?

General vector equation for Relative velocity AvB = Avg - Bvg Note: This vector equation works generally in 1-d, 2-d. and 3-d Check for rear-end approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = Avg - Bvg Use integers to sub AvB = +80 – (+50) = ?

General vector equation for Relative velocity AvB = Avg - Bvg Memorize please! Note: This vector equation works generally in 1-d, 2-d. and 3-d Check for rear-end approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [E] AvB = Avg - Bvg Use integers to sub AvB = +80 – (+50) =30 or 30.0 km/h [E]

General vector equation for Relative velocity Check for head-on approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [W] AvB = Avg - Bvg Use integers to sub AvB = ?

General vector equation for Relative velocity Check for head-on approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [W] AvB = Avg - Bvg Use integers to sub AvB = +80 – (-50) = ?

General vector equation for Relative velocity Check for head-on approach of car and truck: Avg = 80.0 km/h [E] Bvg = 50.0 km/h [W] AvB = Avg - Bvg Use integers to sub AvB = +80 – (-50) = +130 or 130.0 km/h [E]

Harder Example: A truck approaches an intersection at 40. 0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference?

Harder Example: A truck approaches an intersection at 40. 0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = ?

Harder Example: A truck approaches an intersection at 40. 0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E]

Harder Example: A truck approaches an intersection at 40. 0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] What is the symbol for the truck’s velocity with respect to the ground or earth frame of reference?

Given: carvg = 30.0 km/h [E] truckvg = ? Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = ?

Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N]

Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown:

Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ?

Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula:

Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg

AvB = Avg - Bvg or carvtruck = ? Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = ?

AvB = Avg - Bvg or carvtruck = carvg - truckvg Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg

AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute:

AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute:

AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: carvtruck = 30.0 km/h [E] – 40.0 km/h [N]

carvtruck = 30.0 km/h [E] – 40.0 km/h [N] = ? Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: carvtruck = 30.0 km/h [E] – 40.0 km/h [N] = ?

AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? Given: carvg = 30.0 km/h [E] truckvg = 40.0 km/h [N] Unknown: carvtruck = ? Formula: AvB = Avg - Bvg or carvtruck = carvg - truckvg Substitute: carvtruck = 30.0 km/h [E] – 40.0 km/h [N] = 30.0 km/h [E] + 40.0 km/h [S]

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S]

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] 30.0 km/h 40.0 km/h

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] 30.0 km/h 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = ? Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = ? 30.0 km/h 40.0 km/h carvtruck

Harder Example: A truck approaches an intersection at 40. 0 km/h [N] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 30.0 km/h 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h 30.0 km/h 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = ? 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = tan-1(o/a) 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = tan-1(o/a) = tan-1(40/30) 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = tan-1(o/a) = tan-1(40/30) = 53.1° 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = tan-1(o/a) = tan-1(40/30) = 53.1° carvtruck = ? 30.0 km/h Θ 40.0 km/h carvtruck

carvtruck = 30.0 km/h [E] + 40.0 km/h [S] Harder Example: A truck approaches an intersection at 40.0 km/h [N]. A car approaches the same intersection at 30.0 km/h [E]. What is the velocity of the car with respect to the truck’s frame of reference? carvtruck = 30.0 km/h [E] + 40.0 km/h [S] | carvtruck | = (302 + 402)1/2 = 50.0 km/h Θ = tan-1(o/a) = tan-1(40/30) = 53.1° carvtruck = 50.0 km/h [E 53.1°S] 30.0 km/h Θ 40.0 km/h carvtruck

You try this one: A bird is flying at 50. 0 km/h [W] You try this one: A bird is flying at 50.0 km/h [W]. A plane is flying at 120.0 km/h [S]. What is the velocity of the bird with respect to the plane’s frame of reference?

Sub: = 50.0 km/h [W] - 120.0 km/h [S] = 50.0 km/h [W] + 120.0 km/h [N] You try this one: A bird is flying at 50.0 km/h [W]. A plane is flying at 120.0 km/h [S]. What is the velocity of the bird with respect to the plane’s frame of reference? Given: bvg = 50.0 km/h [W] pvg = 120.0 km/h [S] Unknown: bvp = ? Formula: bvp = bvg - pvg Sub: = 50.0 km/h [W] - 120.0 km/h [S] = 50.0 km/h [W] + 120.0 km/h [N] ǀ bvp ǀ = ( 1202 + 502)1/2 Ɵ = tan-1(120/50) = 67.3° = 130.0 km/h bvp = 130 km/h [W 67.3°N] bvp 120.0 km/h Ɵ 50.0 km/h

Relative Velocity Equations

Relative Velocity Equations Review: Do you know the vector equation relating AvB, Avg, and Bvg ?

Relative Velocity Equations Review: AvB = Avg - Bvg relative velocity equation for two objects and ground There is another equation to help us solve problems with relative velocity. This equation is useful when we have many objects involved. Do you know what it is?

Relative Velocity Equations Review: AvB = Avg - Bvg relative velocity equation for two objects and ground Ave = Avb + bvc + cvd + dve ( five objects) This is called the vector chain rule equation

Example: A boat is moving at 14. 0 km/h [E] with respect to the water Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land?

Given: bvw = 14.0 km/h [E] wvL = 11.0 km/h [W] cvb = 5.0 km/h [W] Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] wvL = 11.0 km/h [W] cvb = 5.0 km/h [W] Fvc = 2.0 km/h [E]

Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2

Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown:

Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ?

Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula:

Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = ?

Formula: FvL = Fvc + cvb + bvw + wvL Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = Fvc + cvb + bvw + wvL

Formula: FvL = Fvc + cvb + bvw + wvL Sub: Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = Fvc + cvb + bvw + wvL Sub:

Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 +14 -11 Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 +14 -11

Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 =14 -11 = 0 km/h Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 =14 -11 = 0 km/h

Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 =14 -11 = 0 km/h Example: A boat is moving at 14.0 km/h [E] with respect to the water. The water is moving at 11.0 km/h [W] with respect to the land. A cat on the boat is moving at 5.0 km/h [W] with respect to the boat. A flea on the cat is moving at 2.0 km/h [E] with respect to the cat. What is the velocity of the flea with respect to the land? Given: bvw = 14.0 km/h [E] = +14 wvL = 11.0 km/h [W]= -11 cvb = 5.0 km/h [W]= -5 Fvc = 2.0 km/h [E]= +2 Unknown: FvL = ? Formula: FvL = Fvc + cvb + bvw + wvL Sub: FvL = +2 -5 =14 -11 = 0 km/h Now try #1 on lesson #9 exercises and check your answers!