Uniform Circular Motion & Relative Velocity

Seatwork #2 A man trapped in a valley desperately fires a signal flare into the air. The man is standing m from the base of a vertical 250.0m cliff when he fires the flare with an initial velocity of 100 m/s at an angle 55.0 o from the horizontal. (a) How long does the flare stay in the air? (2 pts) (b) What is the distance from the man and the landing point of the flare? (2 pts) (c) What is the maximum height of the flare? (1 pt) [Ignore air resistance and assume man is very very short. Also assume ground at the top of the cliff is level.]

Other cases for 2D motion at constant acceleration Uniform Circular Motion is defined as a particle moving at constant speed, in a circle.

Acceleration on a Curve

Similar Triangles

Since v and r are constant

Acceleration on a Curve Magnitude of a is constant. But direction is changing and is always pointing inward. We call this kind of acceleration Centripetal Acceleration

Example A sports car has a lateral acceleration of 0.96g’s. This is the maximum centripetal acceleration it can attain without skidding out of a circular path. If the ca is travelling at a constant 40m/s, what is the maximum radius of curve it can negotiate?

Example

Uniform Circular Motion Will be discussed in more depth later on in the semester.

Relative Velocity So far we’ve discussed velocity relative to a stationary point. What happens then if an observer is moving?

A simple example A man is walking at a rate of 1.2 m/s (in the +x direction) on a moving train that has a speed of 15.0 m/s (+x direction) What is the velocity of the man?

A simple example A man is walking at a rate of 1.2 m/s on a moving train that has a speed of 15m/s What is the velocity of the man? 2 observers, someone on the train (A) and someone off the train (B). A will say the man is moving at 1.2 m/s B will say the man is moving at 16.2 m/s Two observers have different frames of reference

Relative Velocity in One Direction 2 observers, someone on the train (A) and someone off the train (B). Denote passenger as (P). We shall define = the velocity of C relative to the frame of D

Relative Velocity in One Direction 2 observers, someone on the train (A) and someone off the train (B). Denote passenger as (P). We shall define = the velocity of C relative to the frame of D

Relative Velocity in One Direction = the velocity of C relative to the frame of D

Relative Velocity in One Direction = the velocity of D relative to the frame of C = the velocity of C relative to the frame of D

Another Example You are driving north on a straight two lane road at a constant 88 kph. A truck is travelling at 104kph approaching you (on the other lane). (a) What is the trucks velocity relative to you? (b) What is your velocity relative to the truck? (c) How do the relative velocities change after you and the truck pass?

Another Example Denote T for truck, Y for you We need a third observer so let it be the Earth E. Given Find

Another Example

Another Example Do the relative velocities change when the truck passes you?

Lets complicate matters A man is walking at a rate of 1.2 m/s (in the +z) direction on a moving train that has a speed of 15.0 m/s (+x direction) What is the velocity of the man?

Lets complicate matters A man is walking at a rate of 1.2 m/s (in the +z) direction on a moving train that has a speed of 15.0 m/s (+x direction) What is the velocity of the man?

Lets complicate matters Instead of walking, the passenger on the train throws a ball straight up into the air and catches is. What path does it take for the passenger? For the observer off the train? Revisit the military helicopter that accidentally dropped a bomb. For the helicopter what was the motion of the bomb? For an observer on the ground?

Example A boat heading due north crosses a wide river with a speed of 10kph relative to the water. The water has a speed of 5.0kph due east relative to the earth. Determine the velocity of the boat relative to the earth. (Compute up to 2 sig figs)

Example

Young and Freedman Problem 3.40 A pilot wishes to fly due west. A wind of 80.0 km/h is blowing due south. If the speed of the plane in still air is 320 km/h, (a) in which direction should the pilot head? (b) what is the speed of the plane over the ground?