# Projectile Motion I - Weebly · PDF file Projectile Motion – Strategy Sheet Most, but...

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Projectile Motion I What is a projectile?

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 GUSx

Motion in the y direction GUSy

Gx Ux Sx Gy Uy Sy

*Remember: down is negative

Projectile motion

GUSx Motion in the x direction

ax = 0 vxf = vxi dx = vxit

GUSy Motion in the y direction

ay = g = -9.81 m/s2

vyf = vyi+gt = -9.81t

dy = vyit+½gt2 = -4.9t2

Illustration: vx and vy 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, vx Vertical velocity, vy 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/s2, 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 GUSx and GUSy tables!!!

Motion in the x direction GUSx

Motion in the y direction GUSy

Gx Ux Sx Gy Uy Sy

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 GUSx and GUSy tables!!!

Motion in the x direction GUSx

Motion in the y direction GUSy

Gx Ux Sx Gy Uy Sy

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 GUSx and GUSy tables.

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.

Motion in the x direction

GUSx Motion in the y direction

GUSy

Gx Ux Sx Gy Uy Sy

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 – vi 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)?]