Question

Time

ground
Xmin=
Ymin=
MY ROCKET'S PROJECTILE MOTION EQUATION IS:
all units in seconds and feet
MY ROCKET'S INITIAL HEIGHT IS:
TIME TO REACH MAXIMUM HEIGHT:
MY ROCKET'S MAXIMUM HEIGHT:
TOTAL TIME IN THE AIR:
Xmax=
Ymax=
distc
time
rocket launch!
y=-(x - 2)² +9
x-intercept: where the
object hits the ground
Height (feet)
motion sketch
time (seconds)

Answer 1

Given the projectile motion equation
`\(y = -(x - 2)^2 + 9\)`, The Initial Height is
`\(y_{\text{min}} = 9\)` , the horizontal Extent
`\(x_{\text{min}} = x_{\text{max}} = 2\)`, the Vertical Extent
`\(y_{\text{min}} = 9\), \(y_{\text{max}} = 9\)`, the time to Reach Maximum Height x = 2, the Rocket's Maximum Height is
`\(y_{\text{max}} = 9\)`, and the Total Time in Air is twice the time to reach the maximum height.

Given the projectile motion equation
`\(y = -(x - 2)^2 + 9\)`, where y represents the height and x represents the horizontal distance, we can determine various parameters:

Initial Height:

`\(y_{\text{min}}\)` is the initial height, which occurs when the rocket is at its starting point. From the equation, we see that the initial height is 9.

Horizontal Extents:

`\(x_{\text{min}}\)` and
`\(x_{\text{max}}\)` are the values of x that correspond to the projectile's motion. Since this is a quadratic equation in the form
`\(-(x - h)^2 + k\)`, where (h, k) is the vertex of the parabola, in this case, (2, 9).

Therefore,
`\(x_{\text{min}} = x_{\text{max}} = 2\)`.

Vertical Extents:

`\(y_{\text{min}}\)` and
`\(y_{\text{max}}\)` are the minimum and maximum values of y, respectively. From the equation,
`\(y_{\text{min}} = 9\)` (initial height) and
`\(y_{\text{max}} = 9\)` (maximum height).

Time to Reach Maximum Height:

The time to reach the maximum height occurs at the vertex of the parabola. In the equation
`\(-(x - 2)^2 + 9\)`, the vertex is (2, 9), and there is no linear term, which means the motion is symmetric. So, the time to reach the maximum height is when x = 2.

Rocket's Maximum Height:

The maximum height is the value of y at the vertex. From the equation, the maximum height is
`\(y_{\text{max}} = 9\)`.

Total Time in Air:

The total time in the air is twice the time it takes to reach the maximum height due to the symmetry of the motion. Therefore, the total time in air is twice the time calculated in step 4.