{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

135_pdfsam_math 54 differential equation solutions odd

# 135_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

Exercises 3.4 Using equation (3.11) and noting that dv/dt = ( dv/dx )( dx/dt ) = ( dv/dx ) v , we can determine the maximum height attained by the shell. With the above substitution, equation (3.11) becomes mv dv dx = ( mg + 0 . 1 v 2 ) , v (0) = 500 . Using separation of variables and integration, we get v dv 10 mg + v 2 = dx 10 m 1 2 ln ( 10 mg + v 2 ) = x 10 m + C 10 mg + v 2 = Ke x/ (5 m ) . Setting v = 500 when x = 0, we find K = e 0 ( 10(3)(9 . 81) + (500) 2 ) = 250294 . 3 . Thus the equation of velocity as a function of distance is v 2 + 10 mg = (250294 . 3) e x/ (5 m ) . The maximum height will occur when the shell’s velocity is zero, therefore x max is x max = 5(3) ln 0 + 10(3)(9 . 81) 250294 . 3 101 . 19 (meters) . 15. The total torque exerted on the ﬂywheel is the sum of the torque exerted by the motor and
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