Solving Projectile Motion Problems

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"Find this stuff." And you're just gonna have to know that okay, if I run off of a cliff horizontally or something gets shot horizontally, that means there is no vertical velocity to start with, I'm gonna have to plug this initial velocity in the y direction as zero. Don't fall for it now you know how to deal with it. But we can't use this to solve directly for the displacement in the x direction.

So we want to solve for displacement in the x direction, but how many variables we know in the y direction? We need to use this to solve for the time because the time is gonna be the same for the x direction and the y direction.

So this is the part people get confused by because this is not given to you explicitly in the problem.

The problem won't say, "Find the distance for a cliff diver "assuming the initial velocity in the y direction was zero." Now, they're just gonna say, "A cliff diver ran horizontally off of a cliff.

And let's say they're completely crazy, let's say this cliff is 30 meters tall. This is a classic problem, gets asked all the time.

And if you were a cliff diver, I mean don't try this at home, but if you were a professional cliff diver you might want to know for this cliff high and this speed how fast do I have to run in order to avoid maybe the rocky shore right here that you might want to avoid.So if the initial velocity of the object for a projectile is completely horizontal, then that object is a horizontally launched projectile. They're gonna run but they don't jump off the cliff, they just run straight off of the cliff 'cause they're kind of nervous. Alright, fish over here, person splashed into the water.Let's say they run off of this cliff with five meters per second of initial velocity, straight off the cliff. So 30 meters tall, they launch, they fly through the air, there's water down here, so they initially went this way, and they start to fall down, and they do something like pschhh, and then they splash in the water, hopefully they don't hit any boats or fish down here. We want to know, here's the question you might get asked: how far did this person go horizontally before striking the water?So if you choose downward as negative, this has to be a negative displacement. Well, for a freely flying object we know that the acceleration vertically is always gonna be negative 9.8 meters per second squared, assuming downward is negative.Now, here's the point where people get stumped, and here's the part where people make a mistake.So a lot of vertical velocity, this should keep getting bigger and bigger and bigger because gravity's influencing this vertical direction but not the horizontal direction. V initial in the x, I could have written i for initial, but I wrote zero for v naught in the x, it still means initial velocity is five meters per second.And we don't know anything else in the x direction.Maybe there's this nasty craggy cliff bottom here that you can't fall on.So how fast would I have to run in order to make it past that?The whole trip, assuming this person really is a freely flying projectile, assuming that there is no jet pack to propel them forward and no air resistance.This person's always gonna have five meters per second of horizontal velocity up onto the point right when they splash in the water, and then at that point there's forces from the water that influence this acceleration in various ways that we're not gonna consider. Vertically this person starts with no initial velocity.