00:01
So for this problem, we have a pot that is falling down towards a man, and we are asked to find the minimum height that the pot can be before, so that this man here below the balcony can dodge or react to this pot falling towards him.
00:24
So this balcony is 20 meters high, and this man is 1 .75 meters tall.
00:30
And his reaction time, it was given to be 0 .3 seconds.
00:39
So our first approach to this problem is to find the time that this man shouts to warn this man below.
00:54
So when this man sends his warning, we know that the error would travel at 3343 meters per second.
01:06
That is the rate at which air travels with time, and we need to take into account this distance here.
01:13
So this distance here will be 20 minus 1 .75.
01:19
So in a sense, we're just using the distance formula, like we did it in a previous problem.
01:24
So the change in x is going to equal velocity times the change in time.
01:35
And this is what we want to solve for is the change in time.
01:38
So let's rearrange our equation to write.
01:40
By dividing velocity to both sides.
01:45
So that will give us the change in distance over velocity, which will then equal.
01:55
So we know our change in distance is 20 meters to 1 .75 meters.
02:02
And we want to use the top of this height because we know his ears is on his head.
02:08
So we're going to estimate that to be 1 .75 meters exactly.
02:12
So 20 meters minus 1 .75 meters, all divided by our velocity, which is the velocity of air travel, 343 meters per second.
02:33
And so because we have a large number here, we should expect to get a very small number.
02:37
And that small number is 0 .053 seconds.
02:49
So that is the time that is how fast the air will travel.
02:58
So the time it takes to alert the man.
03:03
Time to alert the man.
03:15
So now we want to look at, so now that we figured that out, we can look at the time that it will.
03:30
So we know that the reaction time is 0 .3 seconds.
03:34
So we would want to add that to this time here .053 seconds, because if we add these two times, that will tell us the time he needs to react in total.
03:52
So that's the amount of time that has passed while the object is, or by the pot is falling.
04:00
So with that, that will tell us, that will give us the value we need to know.
04:07
To find the distance that the pot needs to be at.
04:10
So our plan is to find the time at which the pot will travel so that we can find the distance it will travel.
04:21
Then we'll also track that with the total distance that it traveled.
04:29
So if we add those two values together, our change in time, let's say our total time, time total will be equal to the reaction time tr plus the change in time.
04:54
So that's just 0 .3 seconds plus 0 .053 seconds.
05:03
And that gives us 0 .35 seconds.
05:09
We could lead that with two significant figures.
05:13
So now that we have this total time, now we need to figure out the time that it takes for the pot to reach the person's head.
05:29
So pot to person.
05:39
So we do this by looking at, we have to use our kinematics equations, which is the change in y is equal to v.
05:51
Of t plus one half g t squared so v or well we know our y is our height so that is our height and velocity our initial velocity is zero because the pot is at rest when it's on the top of the balcony so that goes to zero so that leaves us with the height is equal to 1 1 half g gt squared.
06:27
And this will just tell us, we know g here is gravity.
06:31
So we're finding time it will take for gravity to bring the pot down to the person.
06:38
So now the salt for t, t would then be equal to.
06:46
We'll multiply the 2 to the side and then divide by g...