09SpringHwk03_Soln

09SpringHwk03_Soln - Math 3301 Homework Set 3 Solutions 10...

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Math 3301 Homework Set 3 – Solutions 10 Points 1. (3p ts) Here’s the IVP’s we need for this problem. ( ) ( ) () () () 0 5 0 3 150 7 4 9 4 8 0 50 P r P PP P r P r ¢ = == ¢ = +- = -= Solving the first gives, ( ) ( ) 3 1 3 5 0 15 0 5 0 l n3 r tr P = ee The second IVP is now, ( ) ( ) 1 3 l n 3 8 0 50 P ¢ = The solution is, () ln3 3 24 ln3 28.1542 t Pt =+ e From this we can see that they will survive to take over the world! 2. (3 pts) Here’s the IVP’s for this case. ( ) ( ) 10 2 11 7 5 15 30 2 2 2 22 7 55 9. 8 9. 8 02 9. 8 9. 8 30 c vv v v v vt ¢ =- = ¢ The solution to the first one is, 2 15 1 73. 5 71.5 t - =- e and we’ll need to set this equal to 30 and solve to determine the time when the second parachute opens. 1 5 15 3 0 73. 5 71. 5 0.608 4 3.7269 tt t -- = - fi= &= Eventually we’ll need the “height” function for this so let’s get that and the “height” of the sky diver at this time. () () 1 5 15 1 73. 5 71. 5 0 0 73. 5 536.2 5 536.25 s t d t s s = - = & = ± The sky diver is now ( ) 3.726 9 63.9325 sm = below the plane. The second IVP is now, ( ) 2 222 5 9. 8 3.726 9 30 vvv ¢ = The solution to this one is, 2 5 2 24. 5 24.4226 t - e Next we’ll need the “height” function.
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09SpringHwk03_Soln - Math 3301 Homework Set 3 Solutions 10...

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