00:01
Hello, in this video we will be solving the question i will see on the screen where a basketball player shoots a foul shot releasing the ball at a 45 degree angle from position 6 feet above the floor, 6 feet above the floor.
00:13
And then the path of the ball can be modeled by this function here, where v square, where v is the initial velocity, which is given to us as 27 feet per second, and x is the forward distance from the ball in front of the foul line.
00:28
And our function is for height, height, so we know that h is equal to minus 44 x squared over v square plus x plus 6.
00:38
So we have a quadratic equation in terms of x here.
00:42
And we need to use this equation and initial velocity of 25 feet per second to solve parts a to e.
00:49
So let's first for a look at part a.
00:51
In part a, we're given that we need to determine the height of the ball after it has doubled six feet in front of the foul line.
00:59
So now that we have the x, the value of x, x as 6 we can simply plug the value into our equation so we have x as equal to 6 so our value of h will be equal to minus 44 multiplied by 6 squared which is 36 forward forward 27 squared plus 6 plus 6 again again uh in order to make things easy for us i'm just going to directly add all of this to my calculator so we have 12 minus minus minus 44 multiplied by 36 divided by the square of 27.
01:41
And that's going to give us a value of 9 .83.
01:51
As indicated in the question, i have rounded this off to two decimal places.
01:56
So we have 9 .83 feet as our first answer.
02:00
Let's look at part b now.
02:02
In part b, we need to determine the height of the ball after i has traveled nine feet in front of the foul line.
02:09
Now we have the value of x as equal to 9.
02:12
So we have now 8 equals minus 44 multiplied by the square of x, the square of 9, which will be 81, over again, 27 squared plus 9 plus 6.
02:26
Again, let's simply plug this value into my calculator.
02:30
So we have this time 15 minus 44 multiplied by 81, divided by a 20, divided by a 27 squared and that is going to give us a value of this time 10 .11 where one is a recurring decimal.
02:49
By rounding off to two decimal places, this will be our final onset.
02:54
Let's look at part c now.
02:56
Find the additional points and find additional points and draw off the path of the basketball.
03:01
Now there are two ways we can do this.
03:05
One, we can look at several different points of x and then draw off our point.
03:09
On the the other hand, what we can do is we can look for trends.
03:14
Remember that our equation is the function of x equals minus 44 x squared over v square, where v squared is going to be a constant.
03:26
So let's just directly write 27 squared plus x plus 6.
03:32
Now for graphs like these, it's important to note that we have that this mimics the graph of ax squared plus bx plus c.
03:50
But this time, notice that the coefficient a is negative.
03:55
And when a is negative, our graph generally looks like this...