00:01
In this question, the ball's height is given by the function f.
00:04
And we are asked to find the maximum height the ball reaches and to find the ball's velocity when it hits the ground.
00:12
To find the maximum height, we need to solve the equation as prime of t equals to 0.
00:31
And in our case as prime of t equals to 64 minus 16 times 2 t.
00:38
This equals to 64 minus 32 t.
00:42
And we want this to be equal to zero.
00:48
Note that as prime of t also gives the formula for v of t.
00:52
So this, here, this is basically v of t.
00:57
And since the ball is was thrown up, at some point, it will reach its maximum height.
01:06
And when it reaches its, after it reaches its maximum height, it will start falling down.
01:11
But at the moment, at the moment when it reaches its maximum height, its velocity is going to be zero.
01:16
Right.
01:17
So that's when the ball, ball reaches its maximum height when its velocity equals to 0.
01:23
Now let's solve this equation for t.
01:28
64 minus 32 t equals 0.
01:32
Therefore, negative 32 t equals to negative 64 and t equals to 2.
01:42
So the ball will reach its maximum height after 2 seconds.
01:46
And to determine the height itself, we need to calculate s of 2.
01:51
S of 2 equals to 64 plus 64 times 2.
02:01
Minus 16 times 2 squared by this formula here.
02:11
This equals to 64 plus 128 minus 16 times 4.
02:20
16 times 4 equals to 64.
02:28
64 cancels and we are going to get 128 feet.
02:32
This is a maximum height of the ball.
02:41
Now let's find the...
02:43
Let's answer the second question.
02:45
To find the ball's velocity when it hits the ground.
02:48
The ball hits the ground when its height equals to 0.
02:52
So first we need to solve the equation s of t equals 0...