00:01
All right, we want to calculate the maximum height of a vertical body, and the height is given by the equation, s equals to negative half gt squared plus v initial times time plus s initial, which is the initial height.
00:44
So to do this first, we're going to determine the time at which the height is at maximum.
00:51
And we want to derive with respect to time.
00:58
And we're going to say, well, that is negative half g times 2t plus vt.
01:09
Okay, and then we're going to set that equal to zero to calculate for t.
01:14
And we would say, well, then our 2t is the same thing as negative v -initial, multiplied by negative 2, divided by g, which equals to 2, the initial of g, and then we can cross out the 2s.
01:44
So our time, when height is maximum, is v -initial, divided by gravity.
01:55
Okay, now we can plug that back.
01:57
Back in to our original equation here and we can calculate for when height is at its maximum.
02:10
That would be s equals to negative half g, t squared, which in this case, it's going to be v initial over g squared plus v initial times t, which is going to be v initial over g plus s initial...