Hello Alison,
A. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
When the rocket splashes down into the ocean, it will literally be at sea-level. Therefore, its height will be 0 meters. So to find the splashdown time, you would set h(t) = 0 and solve for t
-4.9t^2 + 187t + 220 = 0
You can either:
- use the quadratic formula, or
-graph -4.9t^2 + 187t + 220 on your graphing calculator and find the x-intercepts (points where the graph crosses the x-axis)
Either way, you should find TWO solutions: one positive and one negative. I got 39.3 seconds and -1.14 seconds. Clearly, negative time is not a realistic solution, so the rocket splashes down after 39.3 seconds
B. How high above sea-level does the rocket get at its peak?
The peak represents the y-coordinate of the vertex of the parabola. There's a formula for the x-coordinate of the vertex. When you have a quadratic function a*x^2 + b*x +c, the x-coordinate of the vertex is equal to -b/(2a).
In the quadratic function given to you: a = -4.9, b = 187 and c = 220.
So x-coordinate of vertex = -187/(2*-4.9) = -187/-9.8 = 19.08 seconds
To find the peak height of the rocket, plug x-coordinate of vertex in place of t:
h(19.08) = -4.9*(19.08)^2 + 187(19.08) + 220 = 2004.13 meters
Therefore: the rocket peaks at 2004.13 meters above sea-level.
