SOLUTION: Solve the following problems by defining the variable, writing a quadratic equation, solving it an then providing a written conclusion.
- A cannonball is fired form ground leve
Question 247743: Solve the following problems by defining the variable, writing a quadratic equation, solving it an then providing a written conclusion.
- A cannonball is fired form ground level on an arc described by h = -t^2 + 28t where "h" is the height in meters at any time "t" in seconds. Determine the number of seconds it would take the ball to reach a height of 192m. At what other point in its flight is also at 192m? Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! A cannonball is fired form ground level on an arc described by h = -t^2 + 28t where "h" is the height in meters at any time "t" in seconds. Determine the number of seconds it would take the ball to reach a height of 192m. At what other point in its flight is also at 192m?
-------------------
h(t) = -t^2 + 28t = 192
t^2 - 28t + 192 = 0
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=16 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 16, 12.
Here's your graph:
--------------
It takes 12 seconds to reach 192 meters.
It's again at 192 meters on its way down at 16 seconds.
--------------
The max height will be at 14 seconds, and the max is 196 meters.
----------------
This must be on a small planet or asteroid to have a gravity of 2 m/sec/sec.
On Earth, it's 9.8 m/sec/sec, and the equation is -4.9t^2 for the acceleration term.