Javelin Problem: Optimal Angle & Speed

[Skipe_]

Homework Statement

A javelin is thrown 90m in an optimal starting angle. Air resistance is not taken into consideration. a) What is the optimal starting angle? b) At what speed does the javelin fly from the thrower's hand?

Homework Equations

The Attempt at a Solution

I really have no clue on this one. Is the optimal starting angle 45°? That would seem somehow logical.

 

[Doc Al]

I really have no clue on this one. Is the optimal starting angle 45°? That would seem somehow logical.

I suspect they want you to derive the optimal starting angle, not just assume it. I assume they mean 'what is the angle that gives the greatest horizontal distance'. This is also called the range of a projectile. But they could mean something else. How does your book define 'optimal starting angle'?

 

[Skipe_]

Yes, i understand what it means. I just don't understand how you can calculate it range being the only given variable.

 

[Doc Al]

Yes, i understand what it means. I just don't understand how you can calculate it range being the only given variable.

If by 'optimal starting angle' they mean 'the angle that gives the greatest horizontal distance', then calculating that has nothing to do with the distance. It's a general result. Your 'logical' guess was correct, but now you must prove it.

This seems like an odd thing to ask as part of a problem, since it's such a general result. What book are you using?

In any case, assuming some unknown speed v and some initial angle theta figure out the range of a projectile. Then solve for the angle that maximizes that range.