

Subject:
Math Problem
Category: Science > Math Asked by: fredewqga List Price: $10.00 
Posted:
04 Dec 2002 16:19 PST
Expires: 03 Jan 2003 16:19 PST Question ID: 119391 
A model rocket is fired from the ground at time t=0 seconds. Its height above the ground is given by the following table. Time(Seconds) Height(Feet) 0 0 3 756 6 1224 9 1404 12 1296 15 900 18 216 2 18.5 a)Find the model h(t),which gives the rocket's height(in feet) as a function of time(in seconds). Remember units! b) Find the derivative model. Remember units! c) Use the model from part a) to complete the table. d)What is the rocket's instantaneous velocity at t=6 seconds? e) What is the rocket's maximun height? When does it reach it?  
 


Subject:
Re: Math Problem
Answered By: blinkwilliamsga on 04 Dec 2002 21:00 PST Rated: 
Hello and thanks for the question! a) The model for the data is: Height (in feet) = 16 * (# of seconds)^2 + 300 * (# of seconds) I used the substitution method to get this result. For an explanation of this technique, see: http://www.ucl.ac.uk/Mathematics/geomath/rev/simnb/sim6.html b) The derivative model is going to be: y' = 32 * (# of seconds) + 300 c) Ok let's complete the table using the model from part (a): For 2 seconds: Height = 16 * 2^2 + 300 * 2 Height = 536 feet For 18.5 seconds: Height = 16 * 18.5^2 + 300 * 18.5 Height = 74 feet d) To calculate the instantaneous velocity we use the derivative model. Feet/second = 32 * 6 seconds + 300 108 feet per second is the instantaneous velocity at 6 seconds. e) For this last part, we can figure out how much seconds passed when the rocket had an instantaneous velocity of zero. This would be the highest point in the rocket's trajectory. To do this we use the derivative model: 0 f/s = 32 * (# of seconds) + 300 # of seconds = 9.375. Therefore, the rocket reached its highest point after 9.375 seconds We can now use the model from part (a) to figure out exactly how high the rocket was: Height = 16 * 9.375^2 + 300 * 9.375 Height (in feet) = 1406.25 Search Strategy: polynomials parabolas solving simultaneous equations If you need clarification on any part please ask before rating this answer. Best of luck! blinkwilliamsga 
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