anonymous
  • anonymous
Algebra 2 Scott launches a model rocket from ground level. The rocket's height h in meters is given by the equation h = -4.9t sq + 56t, where t is the time in seconds after the launch. a) what is the maxium height the rocket will reach? b) how long after it is launched will the rocket reach its maxium height? c) Scott stands on a stool that is 3 meters off the ground to launch the rocket, what is the new height equation? What is the new max height?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
hey is this a calc/derivative problem?
anonymous
  • anonymous
or are you supposed to be solving it in a different way
anonymous
  • anonymous
you can do this with the first derivative

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anonymous
  • anonymous
you want to know when the rate of change of the height is zero, so you take the first derivative
anonymous
  • anonymous
1. h = -4.9t^2 + 56t 2. dh/dt = -4.9*2*t + 56
anonymous
  • anonymous
3. 56 -9.8t
anonymous
  • anonymous
there will be a maximum when that rate is zero
anonymous
  • anonymous
so 56 = 9.8t
anonymous
  • anonymous
t - 56/9.8
anonymous
  • anonymous
errr t = 56/9.8
anonymous
  • anonymous
= 560/98 = 280/49 = 40/7
anonymous
  • anonymous
so at 40/7 seconds, it will reach its highest point
anonymous
  • anonymous
so 40/7 seconds is the correct answer for (B). if you put that back into original height equation, you will have the answer to A.
anonymous
  • anonymous
the answer to C is just 3 meters plus the answer to A
anonymous
  • anonymous
since the rocket still peaks after the same amount of time - just three meters higher
anonymous
  • anonymous
let me know if you were supposed to do this in a different way (eg. graphing)
anonymous
  • anonymous
can you do it graphing? That would be a great help to have both methods.

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