2 Dimensional motion

Relativity of Velocity Theory, developed in the early 20th century, which originally attempted to account for certain anomalies in the concept of relative motion, but which in its ramifications has developed into one of the most important basic concepts in physical science Velocity changes when compared to a frame of reference Velocity can broken down into 2 dimensions. –The vertical (free-fall acceleration) –The horizontal (constant velocity)

Types of Acceleration Acceleration, also known as linear acceleration, rate at which the velocity of an object changes per unit of time. A = v/t ( Average Acceleration) Uniform Acceleration : the constant rate of change in Velocity ( Free Fall ) –9.81 m/s 2 (use 10 m/s 2 in multiple choice)

Vertical And Horizontal Components Horizontal and Vertical components of motion are independent. A Cannon is fired Horizontally from cliff View this from two reference frames: 1.Reference frame moving across. 2.Reference frame on the ground.

Vertical and Horizontal Components #2 the ball follows a parabolic path and remains directly above the launcher at all times As the ball rises towards its peak, it undergoes a downward acceleration In the absence of horizontal forces, there would be a constant velocity in the horizontal direction A ball is projected straight upwards by a launcher located in the bed of the truck

Vertical and Horizontal Components #3 The banana moves in a parabolic path in the presence of gravity The monkey also accelerates downward once he lets go of the limb. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass The Monkey and Zookeeper feeding with a cannon

Formulas

How to choose the best formula Free Fall Acceleration due to gravity Uniform acceleration Distance is not part of the question Time is part of the question

How to choose the best formula Free Fall Acceleration due to gravity Uniform acceleration Distance is part of the question Time is part of the question

How to choose the best formula Choose this formula when the question does not include the TIME

Sample Problem #1 A brick falls freely from a high scaffold at a construction site.  What is the velocity after 4 seconds?  How far does the brick fall in this time?

Solution Given: a = 10 m/s 2 t = 4s V f = 0 m/s + (-10.0 m/s 2 ) ( 4.0 s) = -40 m/s d = 0 m/s (4s) +.5(-10.0 m/s 2 ) (4s) 2 = 0 +.5(-10.0m/s 2 ) (16 s 2 ) = -80m What is the velocity after 4 seconds? Find: V How far does the brick fall in this time? Find: d

Sample problem #2 An airplane must reach a speed of 71m/s for takeoff. If the runway is 1000m long, what must be the acceleration?

Solution (71m/s) 2 = (0 m/s) (a) ( 1000m) (-2000m) a = m 2 / s 2 What is the acceleration needed to take off? Given: V i =0 m/sFind: a =? V f =71 m/s d=1000m a = 2.5 m/s 2

Sample Problem #3 Melanie rolls a.010 kg marble down a ramp and off the table with a horizontal velocity of 1.2 m/s. The marble falls into a cup placed 0.51 m from the table’s edge. How high is the table?

Solution to Problem #3 part 1 Given: d x =0.51m V x =1.2 m/s Find: d y =? Need to find t=? Formula v=d/t 1.2 m/s = 0.51m/t 1.2 m/s = 0.51m/t t = 0.51m / 1.2 m/s t = 0.51m / 1.2 m/s t = 0.43 s t = 0.43 s

Solution to Problem #3 part 2 Given: d x =0.51m V x =1.2 m/s Find: d y =? Found t=.43s Formula d y = 1/2 g t 2 d y = 1/2 (10m/s 2 ) (0.43s) 2 d y = 1/2 (10m/s 2 ) (0.43s) 2 d y = (5m/s 2 ) (0.1849) d y = (5m/s 2 ) (0.1849) d y = 0.92 m d y = 0.92 m

Summary Determine the type of motion List the given information Choose the best formula from the Physics formulas Substitute the proper units Solve for the unknown in the equation