00:01
All right.
00:01
So in this, we're going to solve a bunch of problems using the conservation of energy and the work energy theorem.
00:07
And the first one we'll do is a branch falling from a redwood tree from 95 meters.
00:15
And so the initial height is 95 meters.
00:18
The work done by gravity is going to be mgh or the potential energy that the branch has before it falls.
00:25
And that's going to equal the kinetic energy that it will have when it lands.
00:30
So, this is the change in kinetic energy.
00:34
There's a mass in both terms, so that will cancel out, and we'll be left with v squared is equal to 2gh, so we can multiply through by 2 to get rid of that half.
00:43
So v squared is 2gh, or v squared is the square root of 2gh.
00:49
So if we plug in our value for g and h, we get 43 .2 meters per second.
00:57
The second question has a volcano toss a rock, 525 meters in the air, we need to figure out how fast it was going when it was at the base of the volcano.
01:09
And so for this, we can apply the exact same equation here, where this is the change in potential energy.
01:16
So it's going to go from zero potential energy to this height, and we want to know this speed right here.
01:24
So this is the initial kinetic energy before it gained any potential energy.
01:27
This is the potential energy after it's exhausted, it's kinetic energy.
01:31
So there's a mass in both terms.
01:33
We can cancel those out.
01:35
Take the square root, multiply through by two, and then take the square root.
01:39
And we get a speed of 101 .4 meters per second.
01:45
The third problem has us look at a skier that is skiing on a flat straightaway, where they have an initial speed of 5 meters per second, and a coefficient of friction with the snow of 0 .22...