*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 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.

So this person just ran horizontally straight off the cliff and then they start to gain velocity.

So they're gonna gain vertical velocity downward and maybe more vertical velocity because gravity keeps pulling, and then even more, this might go off the screen but it's gonna be really big. What we know is that horizontally this person started off with an initial velocity.

We don't know how to find it but we want to know that we do want to find so I'm gonna write it there. We know that the, alright, now we're gonna use this 30.

You might want to say that delta y is positive 30 but you would be wrong, and the reason is, this person fell downward 30 meters. They started at the top of the cliff, ended at the bottom of the cliff.This vertical velocity is gonna be changing but this horizontal velocity is just gonna remain the same. In other words, this horizontal velocity started at five, the person's always gonna have five meters per second of horizontal velocity.So this horizontal velocity is always gonna be five meters per second.This person was not launched vertically up or vertically down, this person was just launched straight horizontally, and so the initial velocity in the vertical direction is just zero. They're like "hold on a minute." They're like, this person is gonna start gaining, alright, this person is gonna start gaining velocity right when they leave the cliff, this starts getting bigger and bigger and bigger in the downward direction. We're talking about right as you leave the cliff.That moment you left the cliff there was only horizontal velocity, which means you started with no initial vertical velocity.You might think 30 meters is the displacement in the x direction, but that's a vertical distance.This is not telling us anything about this horizontal distance."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 if something is launched off of a cliff, let's say, in this straight horizontal direction with no vertical component to start with, then it's a horizontally launched projectile. I mean a boring example, it's just a ball rolling off of a table.If you just roll the ball off of the table, then the velocity the ball has to start off with, if the table's flat and horizontal, the velocity of the ball initially would just be horizontal. Let's say this person is gonna cliff dive or base jump, and they're gonna be like "whoa, let's do this." We're gonna do this, they're pumped up.

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