Solving Projectile Motion Problems
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 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?
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.
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.
What we mean by a horizontally launched projectile is any object that gets launched in a completely horizontal velocity to start with.
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.
They want to say that the initial velocity in the y direction is five meters per second.
I mean people are just dying to stick these five meters per second into here because that's the velocity that you were given. That's why this is called horizontally launched projectile motion, not vertically launched projectile motion. The initial velocity in the vertical direction here was zero, there was no initial vertical velocity.