# Range of a Ballista Arrow

joel amos

## Homework Statement

A ballista fires an arrow at an initial velocity of 325 m/s. What is the maximum range it can reach? How high would it get at maximum range? How long would it take?

Rmax = (Vo^2)/g

## The Attempt at a Solution

When I used the formula, I got the maximum range to be 10,778 m. This is close to 6 miles, which is obviously unrealistic. What's wrong here?

azizlwl
1170km/h.
Very powerful ballista.

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joel amos
It's in my text book. But the range equation it R = (Vo^2/g)*sin(2Ɵ). Since firing at an angle of 45 degrees yields maximum range, when theta becomes 45, sin(2Ɵ) is equal to 1 and can be taken out of the formula.

joel amos
1170km/h.

What do you mean by this? That's a velocity, not a distance.

voko
The initial speed given is just above the speed of sound at sea level. Which is completely not realistic for a ballista. But even if it were, the range equation you use would also be unrealistic, because it neglects air resistance. Which cannot be neglected at supersonic speeds.