Free Fall Graphical Method Plot graphs of distance vs time for both balls. It is most important to choose a suitable starting time which is common to both balls. How then would you find the distance between the two balls from the two graphs? Is it consistent with your previous prediction? Algebraic method At some time t during the fall, how would you express the distance traveled by the first ball as a function of time? How would you express the distance traveled by the second balls as a function of time, assuming that it was released at moment Δt after the first one? How would you express the difference in distance between the balls as a function of time? Be careful to define a starting time common to both balls. Is it consistent with your previous prediction? Motion Diagram method Draw motion diagrams of the two falling objects. Place the motion diagrams side by side and pretend that the second ball is released exactly one time step unit after the first. Is it consistent with your previous prediction?

Free Fall Graphical Method Graphs of distance versus time for both balls are in blue Distance between the balls is in red x, m t, s Ball 1 Ball 2

Free Fall Motion Diagram method Draw motion diagrams of the two falling objects. Place the motion diagrams side by side and pretend that the second ball is released exactly one time step unit after the first. Is it consistent with your previous prediction? t=0 t=1 t=3 t=4 t=5 t=2 t=6 Ball 1Ball 2 t=0

Free Fall Again t=0 t=2 t=3 t=4 t=1 t=5 0 X t, s v 9.8m/s 2 t, s x v = gt x = ½ gt 2 a = g H

t=0 t=2 t=3 t=4 t=1 t=5 0 X t, s v0v0 9.8m/s 2 t, s x v = v 0 – gt x = v 0 t – ½ gt 2 a = g H V0V0

Two Dimensions Constant Velocity V water V boat V water x y

Two Dimensions Constant Velocity + Constant Acceleration

Projectile Constant Velocity + Constant Acceleration x y ViVi V ix V iy

Homework (due Monday) Problems Section 2.6 Freely Falling objects #45, 59, 60, 69 Section 3.4 Motion in 2-D # 23, 42

Quiz 1. An elevator moves from the basement to the tenth floor of a building. The mass of the elevator is 1000 kg and it moves as shown in the velocity-time graph below. How far does it move during the first three seconds of motion? 2. The following represents an acceleration graph for an object during a 5 s time interval. Sketch the graph of velocity versus time to represent the object’s motion during the same time interval?