Maximum Height of model rocket

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Homework Statement


A model rocket is launched with an initial velocity of 55 m/s. Its height as a function of time can be modelled by h(t) = -4.9t2 + 55t. Determine the maximum height reached by the rocket.


Homework Equations


h(t) = -4.9t2 + 55t


The Attempt at a Solution



h'(0) = 55, since h'(t) = -4.9(0) + 55 = 55 <-- Height reached within time interval 0 - 1 s

I am not sure how to approach this problem though I assume it has something to do with the initial velocity since it is included in the question. The quadratic formula was used in another problem but it isn't applicable here as far as I can tell. It sounds like I need to find the maximum time or t, in order to be able to find the maximum height. If this isn't possible, would the correct thing be to substitute arbitrary values for time until the height is no longer increasing or positive? If not, I have absolutely no idea.

Any help would be great. Thank you.


* Edit *

Following the logic above it seems like the maximum height would be approximately 153.6 metres after 6 seconds. If this is correct, is there a proper way to express this or find a more precise value for t?
 
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Answers and Replies

  • #2
Ray Vickson
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Homework Statement


A model rocket is launched with an initial velocity of 55 m/s. Its height as a function of time can be modelled by h(t) = -4.9t2 + 55t. Determine the maximum height reached by the rocket.


Homework Equations


h(t) = -4.9t2 + 55t


The Attempt at a Solution



h'(0) = 55, since h'(t) = -4.9(0) + 55 = 55 <-- Height reached within time interval 0 - 1 s

I am not sure how to approach this problem though I assume it has something to do with the initial velocity since it is included in the question. The quadratic formula was used in another problem but it isn't applicable here as far as I can tell. It sounds like I need to find the maximum time or t, in order to be able to find the maximum height. If this isn't possible, would the correct thing be to substitute arbitrary values for time until the height is no longer increasing or positive? If not, I have absolutely no idea.

Any help would be great. Thank you.


* Edit *

Following the logic above it seems like the maximum height would be approximately 153.6 metres after 6 seconds. If this is correct, is there a proper way to express this or find a more precise value for t?

Step 1: plot a graph of the function h(t), to see what is happening.
Step 2: translate the insights from your graph into a formal statement.
 
  • #3
SteamKing
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Homework Equations


h(t) = -4.9t2 + 55t

The Attempt at a Solution



h'(0) = 55, since h'(t) = -4.9(0) + 55 = 55 <-- Height reached within time interval 0 - 1 s

The correct expression for the derivative of the height function is:

h'(t) = -9.8t + 55
 
  • #4
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The correct expression for the derivative of the height function is:

h'(t) = -9.8t + 55

Yeah, oops. I had that written down on paper but messed up here.
 

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