A football is thrown by a quarterback, the footballs height in feet h with respect to time in seconds T can be modeled using your quadratic function. You want to know when the football will be 7.5ft in the air because that's about the right height that your favorite football player would catch the ball. You also want to know if your most despised cornerback in the league will be able to interfere with the catch
After the football was thrown you noticed that it had a height of 7ft but 3 secs later it reached its peak height of 15ft
1)make a function to represent the height of the ball
2)then use that function to find out how long it would take for the football to reach 7.5ft
Assume that the cornerback was 100ft away from the destination of the ball when you 1st noticed the balls height the cornerback can run at a speed of 20ft per second will the cb have time to interfere with the catch if he's running directly towards the balls destination with the receiver
PLEASE EXPLAIN EVERYTHING IN WORDS WITH THE FORMULA IM REALLY CONFUSED
Somebody help
To find a function that represents the height of the ball, we can use the information given.
We know that the ball's height is a quadratic function of time, so it can be represented as h = at^2 + bt + c, where h is the height, t is the time, and a, b, and c are constants.
Let's break down the information given:
1) At t = 0 seconds, the ball's height is 7ft.
This tells us that when t = 0, h = 7. Substituting these values into the equation, we get:
7 = a(0)^2 + b(0) + c
This simplifies to c = 7.
2) At t = 3 seconds, the ball reaches its peak height of 15ft.
This tells us that when t = 3, h = 15. Substituting these values into the equation, we get:
15 = a(3)^2 + b(3) + 7
This simplifies to 9a + 3b = 8. (Equation 1)
Now, let's find the values of a and b by solving a system of equations. We have two equations: c = 7 and 9a + 3b = 8.
From equation 1, we can isolate b:
9a + 3b = 8
3b = 8 - 9a
b = (8 - 9a)/3
Substituting this value of b into equation 1, we get:
9a + 3(8 - 9a)/3 = 8
9a + 8 - 9a = 8
8 = 8
This means that there are infinitely many solutions for a and b, indicating that the original information is not consistent. It's not possible for the ball to have a height of 7ft at t = 0 and reach a peak height of 15ft at t = 3 seconds.
Because the given information is inconsistent, we can't accurately determine the time it would take for the football to reach a height of 7.5ft or if the cornerback will have time to interfere with the catch.
However, if you were to have consistent data about the ball's trajectory, you can use the quadratic function to find the time it takes for the ball to reach a specific height by setting h = 7.5 and solving for t.