00:01
Okay, so we are standing on a cliff here, and this is a height of 50 meters to the ground, and we throw up a ball straight up at 20 meters per second for the velocity.
00:31
For the initial velocity.
00:37
And we know that it's going to go up to some height before it falls back down.
00:42
We'll call that h.
00:44
Okay, and so the first thing we want to do is find the time that it takes to get to the maximum height there, so the top of that h right here.
00:58
All right, so this is part a.
01:00
So all we need to do is use this equation v final equals v initial.
01:09
Plus a t and solve for t so um when we're throwing something up and when it reaches the very top it stops before it falls back down so that means in this case our v final is just zero so we're just taking into account the time from when we start throwing it up until it stops so the v final is at the height h and that's zero and and our v initial is just that 20 meters per second.
01:47
And we are just dealing with gravity.
01:50
So that's going to be negative 9 .81 meters per second squared for the acceleration times t.
02:02
Okay.
02:03
And then we just solve for t, subtract 20 from both sides, divide by 9 .81.
02:14
And then your negatives will cancel.
02:17
On both sides.
02:18
So that gives you 20 meters per second divided by 9 .81 meters per second squared.
02:31
And we get 2 .0 seconds for our time.
02:40
Okay.
02:41
And so then we want to figure out the, let's see, we're looking for the maximum height here.
02:55
So we'll use our other kinematic equation, and we're just working in the y direction, so this is a delta y, the height.
03:05
We'll solve for that, which is going to be our h.
03:09
Okay, so just that distance from where we throw it from, up to the maximum height.
03:14
We're going to figure that out first.
03:17
That's equal to the initial times time, plus one -half acceleration time squared.
03:26
Okay, so let's plug everything in here.
03:31
Okay, so looking for each.
03:33
Our v initial is 20 meters per second.
03:38
We have our time.
03:41
It's two seconds.
03:48
Then minus one -half, 9 .81 meters per second squared.
03:57
So minus because we're dealing with gravity.
04:02
And then plugging in our two over here and make sure that's squared.
04:09
Two seconds.
04:11
Okay.
04:12
And so once we just put that in our calculators, figure out the numbers, we get 20 .4 meters.
04:23
Now that's just age.
04:25
So if you want to know that total height from the ground, so that from the highest point that the ball goes to the ground, that's going to be, so here we'll call this, this whole distance here.
04:49
We'll call that delta y.
04:52
Okay? and so delta y is equal to that 20 .4 plus the 50 meters, meters equals 70 .4 meters and that's just your total distance from the ground or from the ground up to the highest point that the ball goes so there's that and if you're just looking for the height from the starting point up to the highest point that's 20 .4.
05:36
Okay and then in part c, they ask, let's see, they're asking for the time needed for the ball to return to the height from which it was thrown and the velocity at that instant.
05:51
Okay.
05:52
So we're talking about this h distance here.
05:59
So when it gets to this point right here, back down to that point.
06:08
So it goes up and then it goes down.
06:12
So when you're working in the y direction, when you go up and then back down to the same point at which it's thrown, you're going to have the same velocity.
06:24
So the velocity is going to decrease as it gets to the highest point.
06:29
It'll stop.
06:29
And then it'll start increasing on the way down again in the negative direction.
06:35
And so your velocity, your velocity at that point is going to just be negative the velocity that is started at.
06:51
So 20 meters per second, negative 20 meters per second, and the negative just meaning that it's going down now.
06:59
And then the time is also going to be the same time that it took for it to reach the maximum height.
07:06
And it's going back down to that same point.
07:09
So your time here is also two seconds.
07:17
That's how long it took from when you threw it to get to the maximum height, and it's going to take that long to get to that same point again...