Work the Problem As Two One-Dimensional Problems

Physics B Classwork: 2 and 3D Motion Name:______

2-Dimensional Motion Sample Problem Definition: A roller coaster rolls down a 20o incline with an acceleration of 5.0 m/s2. a) How far horizontally has the Examples: coaster traveled in 10 seconds?

Solving 2-D Problems Resolve all vectors into components. Work the problem as two one-dimensional problems. b) How far vertically has the coaster Re-combine the results for the two traveled in 10 seconds? components at the end of the problem.

Sample Problem You run in a straight line at a speed of 5.0 m/s in a direction that is 40o south of west. a) How far west have you traveled in Sample Problem 2.5 minutes? A particle passes through the origin with a speed of 6.2 m/s in the positive y direction. If the particle accelerates in the negative x direction at 4.4 m/s2 a) What are the x and y positions at 5.0 seconds?

b) How far south have you traveled in 2.5 minutes?

b) What are the x and y components of velocity at this time?

5/21/2018 1 Bertrand Projectile Motion Vertical Component of Velocity Something is fired, thrown, shot, or Characteristics: hurled near the earth’s surface.

Horizontal velocity is ______Equations: Vertical velocity is ______

Air resistance is ______

1-Dimensional Projectile Definition:

Launch angle Definition:

Examples:

Why is the launch angle important?

You calculate vertical motion only. Zero Launch angle The motion has no horizontal component. What does a zero launch angle imply?

2-Dimensional Projectile Definition:

Sample Problem The Zambezi River flows over Victoria Examples: Falls in Africa. The falls are approximately 108 m high. If the river is flowing horizontally at 3.6 m/s just before going over the falls, what is the speed of the water when it hits the You calculate vertical and horizontal bottom? Assume the water is in freefall motion. as it drops.

Horizontal Component of Velocity Characteristics:

Equation:

5/21/2018 2 Bertrand Sample Problem Resolving the velocity An astronaut on the planet Zircon tosses Use speed and the launch angle to find a rock horizontally with a speed of 6.75 horizontal and vertical velocity m/s. The rock falls a distance of 1.20 m components. and lands a horizontal distance of 8.95 m Then proceed to work problems just like from the astronaut. What is the you did with the zero launch angle acceleration due to gravity on Zircon? problems.

Sample problem A soccer ball is kicked with a speed of 9.50 m/s at an angle of 25o above the horizontal. If the ball lands at the same level from which is was kicked, how long was it in the air?

Sample Problem Playing shortstop, you throw a ball horizontally to the second baseman with a speed of 22 m/s. The ball is caught by the second baseman 0.45 s later. a) How far were you from the second Sample problem baseman? Snowballs are thrown with a speed of 13 m/s from a roof 7.0 m above the ground. Snowball A is thrown straight downward; snowball B is thrown in a direction 25o above the horizontal. When the snowballs land, is the speed of A greater than, less than, or the same speed of B? Verify your answer by calculation of the landing speed b) What is the distance of the of both snowballs. vertical drop?

5/21/2018 3 Bertrand Projectiles launched over level ground Position graphs for 2-D projectiles These projectiles have highly symmetric characteristics of motion.

Trajectory of a 2-D Projectile launched over level ground Sketch:

Velocity graphs for 2-D projectiles

Characteristics:

Acceleration graphs for 2-D projectiles Range of a 2-D Projectile launched over level ground Definition:

Maximum height of a projectile launched Sample problem over level ground A golfer tees off on level ground, giving Notes: the ball an initial speed of 42.0 m/s and an initial direction of 35o above the horizontal. a) How far from the golfer does the ball Acceleration of a projectile launched over land? level ground Notes:

Velocity of a projectile launched over b)The next golfer hits a ball with the level ground same initial speed, but at a greater angle Notes: than 45o. The ball travels the same horizontal distance. What was the initial direction of motion?

Time of flight for a projectile launched over level ground Notes:

5/21/2018 4 Bertrand Free Response Preparation #1

A cannonball is fired at an angle of 45o above the horizontal at an initial velocity of 77 m/s. The cannon is located at the top of a 120 m high cliff, and the cannonball is fired over the level plain below. a) Draw a representation of the trajectory of the cannonball from launch until it strikes the plain below the cliff. Label the following: A: The point where the projectile is traveling the slowest; B: The point where the projectile has the same speed as it does at launch; C: The point where the projectile is traveling the fastest.

b) Calculate the total time from launch until the cannonball hits the plain below the cliff.

c) Calculate the horizontal distance that the cannonball travels before it hits the plain below the cliff.

d) Calculate the maximum height attained by the cannonball.

5/21/2018 5 Bertrand Free Response Preparation #2

A soccer player on Krypton kicks a ball directly toward a fence from a point 35 meters away. The initial velocity of the ball is 25 m/s at an angle of 40o above the horizontal. The top of the fence is 3.0 meters above the ground. The ball hits nothing while in flight, and, since Krypton has no atmosphere, air resistance is nonexistent. The acceleration due to gravity on Krypton is 12 m/s2. a. Sketch the problem

b. Determine the time it takes for the ball to reach the plane of the fence.

c. Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how far above the fence will it pass?

d. Sketch the horizontal and vertical components of the ball’s velocity as functions of time until the ball reaches the plane of the fence. Draw and label your axes!

e. What is the minimum speed the soccer player must give to the ball if it is to just hit the bottom of the fence at the same time it hits the ground?

5/21/2018 6 Bertrand