00:01
Now in this question, we are giving the height of an object, moving through the air of this, given by this function, right? and then basically we are asked to find object initial velocity, right? while the velocity, of course, is given by, i'm going to read like t, right? that's going to give by the derivative of this function, right? that's what was given by 96 minus 32t, right? now at the initial, the initial velocity, of course, is given by 36, right? you said t equals here, you can 9.
00:31
And the object is the maximum height.
00:33
The maximum height, of course, when the velocity goes to zero, right? so you said the velocity being zero, and you'll find that the t equals 96 over 32, that's three, right? at the two equals two seconds.
00:45
So the maximum height, of course, given by when you put t equal three seconds into this function, you get h3 as the maximum height.
00:55
And that's given by, you know, just just calculated, it's 120, so 112, right, 112 minus 116 times, you know, three squared is nine, right, and plus 96 times three, right? and you'll find this to be given by 112 minus nine times 12 plus three times 96.
01:21
And i found this to be actually given by 292, okay? and they find the object's velocity at the instant, it hits the ground...