What is a projectile? Projectile Motion I A projectile is an object upon which the only force acting is gravity. There are a variety of examples of projectiles. An object dropped from rest is a projectile (provided that the influence of air resistance is negligible). An object that is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible). And an object which is thrown upward at an angle to the horizontal is a projectile, too (provided that the influence of air resistance is negligible). Projectile motion is an example of Motion in the x direction is of motion in the y direction Motion in the y direction is of motion in the x direction 2 dimensions means 2 separate problems! A 1-dimensional motion problem in the x direction A 1-dimensional motion problem in the y direction Fortunately, you already know how to solve 1-D problems!!!
Example: Projectile fired horizontally off a cliff Separate the 2-D problem into two 1-D problems: 2 dimensions 2 separate problems 2 GUS tables: Motion in the x direction GUS x Motion in the y direction GUS y G x U x S x G y U y S y GUS x Motion in the x direction a x = 0 v xf = v xi d x = v xi t GUS y Motion in the y direction a y = g = -9.81 m/s 2 v yf = v yi +gt = -9.81t Projectile motion d y = v yi t+½gt 2 = -4.9t 2 *Remember: down is negative
Illustration: v x and v y at 1-second intervals The important concept depicted in the above vector diagram is that the horizontal velocity remains constant during the course of the trajectory and the vertical velocity changes by -9.8 m/s every second. These same two concepts could be depicted by a table illustrating how the x- and y-component of the velocity vary with time. Time Horizontal velocity, v x Vertical velocity, v y 0 s 20 m/s 0 m/s 1 s 20 m/s -9.8m/s 2 s 20 m/s -19.6 m/s 3 s 20 m/s -29.4 m/s 4 s 20 m/s -39.2 m/s 5 s 20 m/s -49.0 m/s The information in the diagram and the table above illustrate identical points - a projectile has a vertical acceleration of -9.8 m/s 2, and zero horizontal acceleration. The vertical velocity changes by 9.8 m/s each second and the horizontal velocity never changes. This is because there is a vertical force (gravity) acting on the projectile but no horizontal force.
Practice Problem 1: A ball is thrown horizontally off an 80m high cliff with an initial velocity of 30 m/s. How long does it take the ball to reach the bottom? Step 1: Always draw a picture of the situation Step 2: Always use separate GUS x and GUS y tables!!! Motion in the x direction GUS x Motion in the y direction GUS y G x U x S x G y U y S y Answer:
Practice Problem 2: A ball is thrown horizontally off a 100 m high cliff with an initial velocity of 25.0 m/s. How far from the base of the cliff does it land? Step 1: Always draw a picture of the situation Step 2: Always use separate GUS x and GUS y tables!!! Motion in the x direction GUS x Motion in the y direction GUS y G x U x S x G y U y S y Answer:
Projectile Motion Strategy Sheet Most, but not all, projectile motion problems can be solved using the following projectile motion problem-solving strategy: 1. Draw a picture of the situation. 2. Capture the givens and the unknowns in separate GUS x and GUS y tables. Motion in the x direction GUS x Motion in the y direction GUS y G x U x S x G y U y S y 3. Start with the GUS table that contains the unknown from the problem statement. There s a good chance that you ll get stuck because you don t know the time, t. 4. Make the time, t, the unknown in the other GUS table and solve for t. 5. Use the value of t you just found in the first GUS table to solve for the unknown in the problem statement.
Projectile Motion Vocabulary Projectile Horizontal Velocity Vertical Velocity Horizontal Component Vertical Component Dimension 1-D 2-D Independent Resolve a Vector Time of Flight Trajectory Artillery Range Parabola Air Resistance Muzzle Speed
Projectile Motion Problems v i horizontal 1. A cannon fires a shell horizontally at 650 m/s from the deck of a battleship. If the deck is 30 m above sea level, how far does the shell travel before it hits the water? 2. A boy throws a ball horizontally off of a 22 m high vertical cliff. The ball lands at a distance of 18 m from the base of the cliff. What was the initial velocity of the ball as it left the boy s hand?
3. In problem 2 above, how long does it take the ball to hit the ground? 4. What takes longer to hit the ground, a projectile that is dropped off a cliff with an initial velocity of zero, or a projectile that is fired horizontally from a cliff with an initial velocity of 100 m/s? Show all work.
5. Rageaholic Ruthie throws a rotten egg at her noisy neighbor across the alley. Both Ruthie and the noisy neighbor live on the same floor of their respective buildings. The alley is 8 m wide and Ruthie throws the egg horizontally with a velocity of 12 m/s. Does the rotten egg hit the neighbor s window? If not, where on the neighbor s building does it hit? 6. In problem 8 above, what is the horizontal velocity of the egg when it hits the building? What is the vertical velocity? [Extra credit: What is the total velocity (magnitude and direction)?]