Maximum Range of a Ballista Arrow: Accounting for Realistic Factors

[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?

Homework Equations

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.

 

[joel amos]

It's in my textbook. 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.