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Here's a general problem which is a classic 2-dimensional motion problem.
Before we get into it though, let's remind ourselves to the equations
we learned in 1-dimensional motion.
Well, these equations relate a few variables, Δx, initial velocity, time, acceleration, and velocity
which we called some final velocity. I'm going to write those over here.
To fully understand an object's motion in 1 dimension, we like to somehow
decide what the values were for all of these variables.
On 2-dimensional motion, I said which is solving two of these one dimensional problems.
So, we need to make some copies. Δx is going to partner with Δy.
V0 I'm going to call V0x like I did over here to distinguish between whether the velocity
is horizontal or vertical--its prime will be V0y.
There's going to be two accelerations, one in the x direction and
one in the y, likewise two final velocities.
Interestingly enough, however, there is only going to be one time.
There is no x and y version of time because unlike position, velocity, and acceleration,
well, there is no easy way to assign a direction to time.
In physics, we call time a scaler and these other quantities are vectors.
You don't have to worry about the vocabulary for now.
If we want to know the trajectory of this ball as it travels through the air,
our goal is to get numerical answers for each these quantities.
Some, we can already fill in. V0x I know be 10 meters per second.
This is the number that I just gave you at the start of the problem.
What about Δy? Can you tell me what delta y would be in meters?
Well, that's the vertical distance the ball is going to move
over the course of it's trajectory and that's exactly equal to 50 meters.
What about this acceleration of 10 meters per second squared?
Is that a horizontal or a vertical acceleration?