SOLUTION: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t^2+169t+234. Assuming that the rocket will splash

Question 1136201: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by
h(t)=−4.9t^2+169t+234.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after
seconds.[Round your answer to 4 decimal places)
How high above sea-level does the rocket get at its peak? [Round your answer to 3 decimal places]
The rocket peaks at
meters above sea-level.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
NASA launches a rocket at t=0 seconds.
Its height, in meters above sea-level, as a function of time is given by
h(t)=−4.9t^2+169t+234.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
When splash down occurs, h(t) = 0, therefore
-4.9t^2 + 169t + 234 = 0
find t using the quadratic formula; a=-4.9, b=169, c=234

do the math, I a positive solution of
t = 35.8229
The rocket splashes down after 35.8229 seconds.[Round your answer to 4 decimal places)
:
How high above sea-level does the rocket get at its peak? [Round your answer to 3 decimal places]
The max occurs on the axis of symmetry, use x=-b/(2a) to find it
t =
t = 17.2449 sec
replace t with 17.2449 in the equation
h(t) = -4.9(17.2449^2) + 169(17.2449) + 234
do the math, I got
1691.194
The rocket peaks at 1691.194 meters above sea-level.
graphically

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