Speed at which to hurl a projectile?

[vabtzeexo]

Homework Statement

The Archimedes' catapult could hurl a 77 kg stone a distance of 180 m. What was the stone's initial velocity as it left the catapult? The wind resistance is assumed to be insignificant.

Homework Equations

$$y = v_y0 t - (1/2) g t^2$$
$$x = v_x0 t$$

The Attempt at a Solution

I think the mass of the stone is irrelevant as wind resistance is not taken into account. The problem would be easy if I knew the angle at which the catapult was fired. Here, however, both the angle and the initial velocity of the projectile are unknown. The answer provided by the textbook says the velocity is > 42 m/s. So clearly the 42 m/s is the initial velocity at the optimal angle and if you change the angle, you have to make up for it by launching at a greater initial velocity. I think the solution might have something to do with a derivative function, but other than that, I'm completely lost.

 

[Redbelly98]

Welcome to Physics Forums.

There is an optimal angle, which gives the maximum range for a projectile launched from ground level. Perhaps your book has a discussion of "range" in the section on projectile motion?

 

[vabtzeexo]

Thanks. I figured it out now. So apparently the optimal angle is always 45 degrees.

 

[Redbelly98]

Yes. Glad it worked out.