Attempted Part I & II Problems

[theredbarronmvr]

Homework Statement

A bullet of mass m is shot vertically up with initial speed v0. It is subject to air resistance that is quadratic in speed (constant of proportionality c2).

i. What is the maximum height reached?

ii. What initial speed u0, would be necessary to reach the same maximum height in the absence of air resistance?

Express your answers in terms of c2, g, m, and v0.

Relevant Equations

For part i: m(dv/dt) = -c2(v^2) - mg

I have an attempted solution to part i here. I'm primarily having trouble with part ii since I don't see how the x found in part i can be attained if there's no air resistance term.

 

[PeroK]

I'm primarily having trouble with part ii since I don't see how the x found in part i can be attained if there's no air resistance term.

If there is no air resistance, then it's a simple projectile motion problem.

 

[theredbarronmvr]

If there is no air resistance, then it's a simple projectile motion problem.

Ahh of course, thank you! I was definitely overthinking it.

 

[vela]

I have an attempted solution to part i here. I'm primarily having trouble with part ii since I don't see how the x found in part i can be attained if there's no air resistance term.

In case you're wondering, when you evaluated the integral, you assumed $c_2 \ne 0$, so it isn't valid to set $c_2=0$ in the expression you derived. (I assume that's the difficulty you were running into.) You have to set $c_2$ to 0 before you integrate.