Maximum Range of a Ballista Arrow: Accounting for Realistic Factors

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In summary, the conversation discusses the maximum range, height, and time of a ballista firing an arrow with an initial velocity of 325 m/s. The formula used to calculate the maximum range is Rmax = (Vo^2)/g, which yields a range of 10,778 m. However, this range is considered unrealistic due to neglecting air resistance and the initial speed being above the speed of sound. The range equation used, R = (Vo^2/g)*sin(2Ɵ), also neglects air resistance and yields a velocity of 1170km/h at an angle of 45 degrees. This velocity is considered unrealistic for a ballista.
  • #1
joel amos
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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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  • #2
1170km/h.
Very powerful ballista.
 
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  • #3
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.
 
  • #4
azizlwl said:
1170km/h.

What do you mean by this? That's a velocity, not a distance.
 
  • #5
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.
 

FAQ: Maximum Range of a Ballista Arrow: Accounting for Realistic Factors

What is the range of a ballista arrow?

The range of a ballista arrow can vary depending on multiple factors such as the type of ballista, the weight and size of the arrow, and the angle at which it is fired. Generally, the range can be anywhere from 500 to 1000 yards.

What is the maximum distance a ballista arrow can travel?

The maximum distance a ballista arrow can travel is around 2000 yards. However, this is only achievable with a specialized ballista and a very lightweight arrow, and it is not recommended as it sacrifices accuracy and power.

What factors affect the range of a ballista arrow?

The range of a ballista arrow can be affected by the wind speed and direction, the weight and size of the arrow, the angle at which it is fired, and the type and condition of the ballista. The terrain and weather conditions can also have an impact.

How accurate is a ballista arrow at long distances?

At longer distances, the accuracy of a ballista arrow decreases due to factors such as wind resistance, gravity, and the weight of the arrow itself. However, with precise calculations and adjustments, a skilled ballista operator can still achieve a decent level of accuracy.

Can a ballista arrow be fired at a specific target?

Yes, a ballista arrow can be aimed and fired at a specific target. This requires a skilled operator who can adjust the angle and direction of the ballista, as well as consider external factors such as wind and gravity to hit the intended target.

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