Riddle

• How can you throw a ball as hard as you can and have it come back to you even if it doesn't hit anything there is nothing attached to it and no one else catches or throws it?

Relative Motion

Relative Velocity

Velocity of A relative to B: VAB=VA-VB

vAB : v of A with respect to BvB : v of B with respect to a reference frame (ex.: the ground)vA : v of A with respect to areference frame (ex.: the ground)

Example 1

• The white speed boat has a velocity of 30km/h,N, and the yellow boat a velocity of 25km/h, N, both with respect to the ground. What is the relative velocity of the white boat with respect to the yellow boat?

•Answer: 5km/h, N

Example 2- The Bus Ride

A passenger is seated on a bus that is traveling with a velocity of 5 m/s, North.If the passenger remains in her seat,what is her velocity: a) with respect to the ground? b) with respect to the bus?

Example 2 -continued The passenger decides to approach the

driver with a velocity of 1 m/s, N, with respect to the bus, while the bus is moving at 5m/s, N.

What is the velocity of the passenger with respect to the ground?

Answer: 6m/s, N

Resultant Velocity

The resultant velocity is the net velocityof an object with respect to a referenceframe.

Part II

• Constant velocity in each of two dimensions (example: boat & river, plane and wind)

Velocity of Boat in Still Water

Velocity of River

with respect to the ground

Example 4-Airplane and Wind

An airplane is traveling with a velocity of 50 m/s, E with respect to the wind. The wind is blowing with a velocity of 10 m/s, S. Find the resultant velocity of the plane with respect to the ground.

Answer: 51m/s, at 11o below the + x axis (E).

Independence of Vector Quantites• Example: The constant velocities in each of the

two dimensions of the boat & river problem, are independent of each other.

Velocity of Boat in Still Water

Velocity of River

with respect to the ground

Example 5- Boat and River

A boat has a velocity of 4 m/s, E, xin still water. It is in a river of width 150m, that has a water velocity of 3 m/s, N.

a) What is the resultant velocity of the boat relative to the shore.

b) How far downstream did the boat travel?

Answer: a) 5m/s, @ 37o above + x axis (E) b) 113m

Test Practice

• Pg. 76: 11, 13

• Pg. 78: 20, 21, 22, 23, 32,

• Pg. 79: 37

• Pg. 80: 56, 59

• Pg. 83: 88, 90

• How much dirt is in a hole 3 ft by 4 ft wide?

• John ordered a fishing rod, priced at $3.56. Unfortunately, John lives in a remote part of Greenland and the import rules there forbid any package longer than 4 feet to be imported.The fishing rod is 4 feet 1 inch long. How can

John get his fishing rod shipped to him without breaking the rules. Ideally the rod stays in one piece.