00:01
Okay, so for this coin dropped out of a hot air balloon, the hot air balloon itself is moving upward at 10 meters per second, and the coin is dropped when it's 300 meters above the ground.
00:11
Now, the movement of the hot air balloon is the same movement as the coin until it's released.
00:18
And so that means this coin also has an initial velocity of 10 meters per second upward once it's released.
00:24
Now, the first question asks, what is its maximum height that it gets to? so if it's traveling upward at 10 meters per second, even once it's let go, it's going to continue traveling upward as gravity slows it down until it momentarily stops and then plummets downward.
00:41
So we use the equation v squared equals initial velocity squared plus two times a times x.
00:47
And the final velocity in this case is zero, because if it's the coin's maximum height, that's where it momentarily comes to a stop before it starts to fall.
00:57
So when we solve that, we find that it changes its position by 5 .1 meters.
01:03
Now that means compared to the ground, if it changed its position 5 .1 meters starting at 300 meters, its total maximum height is 305 meters off the ground.
01:14
The second part of this problem says at four seconds, what is its position in the air, and how fast is it going? so now we have to look at its initial velocity is still positive 10 meters per second, and it still starts 300 meters above the ground, but now we have a time for four seconds.
01:32
So to solve for the position, we use position equals initial position plus initial velocity times time, plus one -half acceleration times time squared.
01:40
And we have all of these pieces, so we plug it in, we find that after four seconds, this point is 262 meters above the ground.
01:48
To solve for velocity, that's pretty straightforward...