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Physics - Projectile Motion Cheat Sheet by

For the test that I don't wanna take :(

Vocabulary

projectile
object moving through the air, either initially thrown or dropped, subject only to the effects of gravity
tragectory
the path of a projec­tile, which is parabolic in two dimensions
projectile motion
movement of an object through the air, subject only to the effects of gravity
range
the maximum horizontal distance a projectile travels
launch angle
The angle of a projec­tile’s initial velocity when measured from the horizontal direction. These angles are typically 90° or less

Kinematic Equations

 

Common Mistakes and Miscon­cep­tions

1.) Reme­mber: What happens in the vertical direction does NOT affect the horizontal direction, and vise versa.
- An object's horizontal position, velocity, or accele­ration does not affect it's vertical position, velocity, or accele­ration. These variables are only related by t time.

2.) It's easy to forget that horizontal motion has constant velocity (and zero accele­ration) while vertical motion has constant accele­rat­ion
- This means for projectile motion, the initial velocity in the x-dire­ction will be the same as the final velocity in the x-dire­ction, while the starting and end velocities in the y-dire­ction will be different because of accele­ration due to gravity.

3.) Make sure to define the coordinate axes and pay attention to the sign of the accele­ration constant g.

How to Solve (Launched at an Angle)

1.) Draw a diagram of the scenar­io
- Make sure to label everything or Brian will be mad

2.) List our known and unknown variab­les
- Make a T-chart with an x and y column where you fill out the variables

3.) Break the motion into horizontal and vertical components parallel to the x and y-axes
- Motion in each dimension is indepe­ndent of each other

4.) Solve for the unknowns in two separate motions - one horizontal and one vertic­al.
- Use the kinematic equations to solve. Usually, try to find time first because that will make everything easier. Time is the common variable between the x motion and y motion

When solving for the initial veloci­ties, you have to use trig, so x would be the initial velocity times cosθ and y would be the initial velocity times sinθ
 

How to solve (Horiz­ontal Projec­tiles)

1.) List our known and unknown variab­les
- make a t-chart with an x and y column where you fill out the variables

2.) Break the motion into horizontal and vertical components parallel to the x and y-axes
- Motion in each dimension is indepe­ndent of each other

3.) Solve for the unknowns in two separate motions - one horizontal and one vertic­al.
- Use the kinematic equations to solve. Usually try to find time first because that will make everything easier. Time is the common variable between the x motion and y motion

Tips (Horiz­ontal Projec­tiles)

- Um just make sure to always find time first because that makes everything a lot easier. Usually, if you want to find time, the equation is D=Vi+(­1/2­)t

- Also, you usually know the initial and final velocities for the x-axis, so write that in the T chart. They should both be the same, so that means accele­ration is 0. If there are any other variables that are given, write them in the T chart. As for the y-axis, accele­ration should be -9.8 m/s2. Again, time is the same for both x and y (unless it's some weird problem)

- The final velocity for y, when it reaches the vertex, is 0 m/s^2

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