Confused by first question in air resistance problem

[errubio]

Homework Statement

all information is on picture

Homework Equations

The Attempt at a Solution

I read the paper and understood it but when I got to the first question I was really confused. I do not even know what the problem is asking. This problem could give me an A in the class but its confusing the hell out of me. where did the e come from. If anyone can give me any hints or anything I would really appreciate it. I have worked on it for about 2 hours and I cannot figure it out. Please help

 

[errubio]

I end up with Vx=e^(-Yt) where Y=b\m
But i don't know where the cosine comes from for part 1

 

[sophiecentaur]

I end up with Vx=e^(-Yt) where Y=b\m
But i don't know where the cosine comes from for part 1

Are you familiar with adding vectors together and with splitting a vector into horizontal and vertical components?

 

[Rayquesto]

for the first part, where

V,x(t)=V0costheta(e^-gamma(t)) I would search up the true definition of e. I believe it has to do with taking the limit as n->infinity of (1 +r/n)^1/n, but I think I'm wrong. Once you gather this information, think about it's meaning and relate it to this problem to prove that this is true.

 

[Rayquesto]

oops I was close:
e = limn->infinity (1 + 1/n)^n.
http://mathforum.org/dr.math/faq/faq.e.html
where let's say you have V0 then V=V0(1+a/n)^nt if P=P0(1+r/n)^nt=P0(e^rt)due to the limit as n approaches infinity.

Don't quote me on this one, but just try to reason this analysis out to provide a thoughtful proof that makes logical sense.

 

[Rayquesto]

I'd then relate this analysis to euler's method. You know what that is right? I mean I hardly do, but this limit as n approaches infinity seems analogous to euler's method.