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# Physics - Projectile Motion Cheat Sheet by BeeBooBopNerd

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

### 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=Vit+(1/2)at`` ``- 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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