00:01
A ball upward.
00:03
And we want to know at what time is it below a certain height.
00:10
So we want to know where this ball is below 100 feet if we threw it at 200 feet.
00:16
And so now we are given a height function, but we want to know where that height is less than 100.
00:26
And so if we have the quadratic or we have the function of the height, we want to know where it's less than 100.
00:32
We can figure out where we can manipulate that and say, okay, so we have, we have negative 16 t squared, negative 16, negative 16 t squared plus 40t.
00:55
And then since we subtracted 100 to get it to make the height less than zero.
01:03
So we have plus 100 is less than 0 feet.
01:14
And so now we can solve using the quadratic formula.
01:17
So we have negative 40 plus or minus plus or minus the square root of b squared, which is 16, which is 16.
01:31
100 minus 4 times negative 16 4 times negative 16 times 100 so that's plus 6400 plus 6400 plus 6400 over 2 times negative 16 negative 30 and so if we were to solve for this we would get we would get the root of the square root of 1 ,600 plus 6 ,400 is the same thing as saying is the same thing as saying the square root of 8 ,000.
02:24
So the square root of 8 ,000 is 89 .442, but if we say negative 40 plus this value, so if we were to solve this, we can figure out the values of t.
02:37
Say, let's say t is equal to, well we have negative 40 plus 89 .442 which is a square of 8 ,000...