Range of a Ballista Arrow

1. Sep 25, 2012

joel amos

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
Rmax = (Vo^2)/g

3. 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?

2. Sep 25, 2012

azizlwl

1170km/h.
Very powerful ballista.

Last edited: Sep 25, 2012
3. Sep 25, 2012

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.

4. Sep 25, 2012

joel amos

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

5. Sep 25, 2012

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.