solution_2.9

# solution_2.9 - Solutions 2.9 1 We have the differential...

This preview shows pages 1–2. Sign up to view the full content.

Solutions 2.9 1. We have the differential equation v 0 = - g - k m v, v (0) = 0 , which has the solution v ( t ) = - mg k + mg k exp( - kt m ) . The velocity is half of the terminal velocity when exp( - kt m ) = 1 2 , i.e. t = m k ln 2. 2.a) We have mv 0 = - kv, hence v ( t ) = v (0) exp( - kt m ) . We are told that v (0) = 220 mph, t = 4 sec, v ( t ) = 50 mph, and mg = 3000 lb. Since g = 32 ft/sec 2 , we find m = 93 . 75 lb sec 2 /ft. Finally k = m t ln( v (0) /v ( t )) = 34 . 73 lb sec / ft . b) The distance traveled is Z 4 0 v ( t ) dt = v (0) m k (1 - exp( - 4 k m )) = 0 . 1274 miles . (Do not forget the conversion from hours to seconds here!) 4. We have mv 0 = - mg - kv, v (0) = v 0 . The solution of the differential equation is

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern