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 |
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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.
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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 |
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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
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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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