Given range and angle - but not time - find initial velocity?

[exi]

Homework Statement

Given a missile with 9500km range, what must its initial velocity be to travel that distance? Disregard issues introduced by the missile's boost phase, and state the velocity as km/h.

(Presumably, the curvature of the planet is to be ignored, as well.)

Homework Equations

Unsure; see below.

The Attempt at a Solution

If a missile is to have maximum range, then its launch angle ought to be 45°. It would also have a symmetrical trajectory and is affected by gravity at -9.8 m/s^2 (or 0.0098 km/s^2 in the terms of this problem).

The first thing that came to mind was to use R=Vo^2/g*sin(2*45) and solve for Vo, but that yielded something ridiculously slow for that long of travel.

I'm rather unsure as to which equation(s) ought to be used to solve such a problem, since everything I can find written in my notes refers to what appear to be slightly different situations.

 

[Doc Al]

The first thing that came to mind was to use R=Vo^2/g*sin(2*45) and solve for Vo, but that yielded something ridiculously slow for that long of travel.

What did you get?

 

[exi]

What did you get?

I did it the first time without converting acceleration and had 300something km/h, or 186 mph.

The second time with the conversion worked out to like 93.1 km/h, which ... well, a 57 mph missile isn't going to travel 6,000 miles.

 

[Doc Al]

You might want to redo your calculation--you're way off. Be sure you use standard units and then convert to km/h.

 

[exi]

You might want to redo your calculation--you're way off. Be sure you use standard units and then convert to km/h.

Yeah, so I am. 9.6488 km in a second sounds more like it (and is correct). Looks like my bad habit of neglecting units in figures bit me in the ass for once.

Thanks again. This place is becoming my home away from physics lecture home, I swear.