Projectile Motion

by Jared Rovny

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    00:01 We're now going to move to one of the most prominent examples of a physics problem in 2 dimensions, and that is projectile motion.

    00:07 Projectile motion is just the fancy way to say that we throw something or launched something into the air at some angle from the ground so that it launches up as you can see here and sort of follows the characteristic of parabolic path.

    00:19 All kinds of things could be asked about this sort of situation.

    00:23 But let's first just do a quick overview of the physics, of a scenario like this one, and what the different variables, variables of motion, in our equations of motions would look like.

    00:33 First of all it it's in the air and it's near the surface of the earth, the earth is pulling it down and that's why it's falls.

    00:38 And so we say that the acceleration of this object because of the pull of the earth, is g in magnitude, which is 9.8 meter per second squared and its downwards in direction, and so we give it a negative sign because again, it is pointing downwards. So in a projectile motion problem near the surface of the earth until we get into more complicated gravity equations, near the surface of the earth, you can always assume that something will have a gravitational acceleration of g, where 9.8 meters per seconds squared downwards.

    01:07 What we do to solve a problem like this is, since it isn't 2 dimensions to make it simpler.

    01:12 That is how we solved this problem.

    01:13 It's just we can't do a 2 dimensional problem, so we just make it into two 1 dimensional problem.

    01:17 So we have this arrow, this red arrow pointing off at an angle, which means that it's hard to tell how much of it is up, and how much of it is sideways.

    01:25 So the very first thing we always do in a problem like this is to break it up into components just like we saw with the vector before.

    01:33 So, we consider the horizontal aspect of the motion and we'll consider the vertical aspect of motion and we'll keep them completely separate from each other.

    01:40 Not let them mix at all because we know how to solve 1 dimensional problems.

    01:44 So first, going through our horizontal equations, the horizontal variables that we have, we have no acceleration on the horizontal direction.

    01:54 This is just because left and right we haven't introduce any air resistance or anything like this, so nothing that's trying to speed up or slow down your object from the moment it's been launched.

    02:02 We launched it and then after that there's nothing pushing it or pulling it in the horizontal direction.

    02:07 The velocity of the object in the horizontal direction, just using our equations of motion and plugging in a zero for the acceleration, is just going to be whatever initial velocity it had in the horizontal direction.

    02:19 This makes sense if we have no acceleration, whatever velocity in initially had it will continue to have throughout the entire problem.

    02:25 And again, this is just in the horizontal direction.

    02:28 The position we can find in the exact same way by going through our equations of motion and plugging in a zero for the acceleration in the horizontal direction.

    02:37 Plugging in that zero we see we have the initial position plus the velocity in the x horizontal direction times the time. In the vertical direction, it's a little more complicated because we do have an acceleration. We have acceleration of minus g, or 9.8 meter per second downwards.

    02:53 So we'll plug this instead into our equations of motion and get a velocity that is v minus gt, remember to put in that minus sign in there for the gravitational acceleration, and then we have a position which also depends on this acceleration in the way given to us by the equations of motion.

    03:08 So the vertical position is equal to its initial vertical position plus the initial vertical velocity, times the time, minus 1/2 the gravitational acceleration times the time squared.

    About the Lecture

    The lecture Projectile Motion by Jared Rovny is from the course Translational Motion.

    Included Quiz Questions

    1. It is always downwards and unchanging in magnitude.
    2. It is downwards except right at the top of its flight.
    3. It is positive on the way up and negative on the way down.
    4. It is positive until the projectile hits the ground.
    5. It is always downwards and changing in magnitude.
    1. You can treat them separately.
    2. They add like scalar measurements.
    3. You cannot treat them separately.
    4. The horizontal and vertical components depend on different time variables.
    5. The components become identical.
    1. The horizontal acceleration is zero in the absence of air resistance.
    2. The initial velocities in each direction are equal.
    3. The initial horizontal velocity is always zero.
    4. The initial vertical acceleration is always zero.
    5. The vertical acceleration decreases during motion.

    Author of lecture Projectile Motion

     Jared Rovny

    Jared Rovny

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    great and traightfoward
    By Chandler P. on 26. November 2017 for Projectile Motion

    Great and straightforward lecture For short period of time. Thank you very much