00:01
For this problem to begin i'll say that we can reasonably assume that there is no horizontal acceleration, but there is a vertical acceleration of negative 9 .8 meters per second squared due to gravity.
00:17
So knowing that we can then consider the two components of our motion, x and y.
00:23
For understanding our position in x as a function of time, it'll be equal to our initial position along x plus our x velocity times time.
00:36
For understanding our y position, or our vertical position, y of t, it'll be our initial position of y plus v y t plus one half a y t squared.
00:57
Now to begin i'll note here that it doesn't say how high the ball is initially thrown from, so because of that i'm going to assume that we are throwing from a height of zero and that, or basically we are throwing from the ground and we'll consider that our initial height, whenever we return to our initial height, that means that we have hit the ground, because otherwise we just don't have enough information to actually answer the question.
01:26
That being said, let's see here, maximum height reached by the ball.
01:34
So if we consider, now i'll note that there are a few different ways to think about this, but one way to think about it is that we do have a situation where we have a parabolic shape for our vertical trajectory.
01:52
Now one thing that i'll note, this might be a situation where it's going to depend on essentially whether you are doing a physics class after you've learned calculus or not.
02:04
The idea is that if we differentiate, that's the calculus idea, if we take the derivative of y with respect to t, that gives us our vertical velocity as a function of time.
02:16
So i'll write that as y dot of t.
02:19
That will be our initial vertical velocity plus our acceleration times time.
02:27
So to find the point in time when we reach this turning point we want to solve for when our vertical velocity is equal to zero.
02:36
So that would be when ay, t, is equal to negative vy, or when t is equal to negative vy divided by ay.
02:49
We know that vy, that was our initial velocity, is going to be, oh actually one second here, so we know that the overall velocity was 20 meters per second initially.
03:01
It was thrown at an angle of 30 degrees above the horizontal.
03:07
So applying our cosine, or applying our sine rules, or pardon me, trigonometric ratios, that's the term i should have been using...