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A model rocket is launched off the top of a platform. The height of the rocket is given by the function h(t) = -4.9t2 + 86t + 2.1, where h(t) is the height in metres and t is the time in seconds.
a) When will the rocket’s height be 200 m?
b) How long will it take for the rocket to reach the ground?

Julius  Apr 4, 2017
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a)   200 =  -4.9t^2 + 86t + 2.1     subtract 200 from both sides

0  =  -4.9t^2 + 86t - 197.9    using the quadratic formula.....we have

t  =    [ -86 ± √ [ (86)^2  - 4 ( -4.9) (-197.9) ] ]  /  (2 * - 4.9)

Evaluating this.....we have that ....   t  ≈ 2.7 seconds  and t ≈ 14.8 seconds

b)  0  = -4.9t^2 + 86t + 2.1

Again, using the quadratic formula we have  ≈    17.575 seconds

CPhill  Apr 4, 2017

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