- #1

- 148

- 38

- Homework Statement
- Finding the range of an object shot from a canon with air resistance of the form -k*m*v

- Relevant Equations
- Series expansion

So I'm on page 67 of Marion/Thornton's "Classical Dynamics of Particles and Systems" and I'm in need of some help. I understand that so far there's is an equation that cannot be solved analytically (regarding motion due to the air resistance and finding the range of the an object shot from a canon). So we got to take a series expansion of the exponential to help with this.

The problem is that I cannot for the life of me see how to arrange the terms to get the forms the author uses. Specifically I'm mystified about how 2.45 is coaxed into 2.47 using 2.46, and how 2.47 is made into 2.49 using 2.48.

The problem is that I cannot for the life of me see how to arrange the terms to get the forms the author uses. Specifically I'm mystified about how 2.45 is coaxed into 2.47 using 2.46, and how 2.47 is made into 2.49 using 2.48.