Maximum Range of a Ballista Arrow: Accounting for Realistic Factors

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Homework Help Overview

The discussion revolves around calculating the maximum range of a ballista arrow fired at an initial velocity of 325 m/s. Participants are examining the implications of this velocity and the realism of the resulting calculations in the context of projectile motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of different equations for maximum range, including one that incorporates the angle of launch. Questions arise regarding the realism of the initial velocity and the effects of air resistance at high speeds.

Discussion Status

The conversation is ongoing, with participants questioning the assumptions made about the initial speed and the applicability of the range equations used. Some guidance has been offered regarding the angle of launch and the need to consider air resistance, but no consensus has been reached.

Contextual Notes

There is a noted concern about the initial speed being supersonic, which raises questions about the validity of the calculations and the neglect of air resistance in the equations being applied.

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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?
 
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1170km/h.
Very powerful ballista.
 
Last edited:
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.
 
azizlwl said:
1170km/h.

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

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