SOLUTION: A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following, h = 50t - 5(t,s) Find all t

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Question 1186378: A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following,
h = 50t - 5(t,s)
Find all the values of t for which the rocket's height is 30 meters.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following,
h = 50t - 5(t,s)
-----
Find all the values of t for which the rocket's height is 30 meters.
======================
IDK what (t,s) means.
-----
h(t) = 50t - 5t^2 = 30
-t^2 + 10t - 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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=76 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.641101056459326, 9.35889894354067. Here's your graph:

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t = smaller value ascending, larger value descending



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