Enter the initial velocity, launch angle, and acceleration due to gravity into the calculator to determine the range of the catapult.
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Catapult Range Formula
The following formula is used to calculate the range of a catapult for a given initial velocity, launch angle, and acceleration due to gravity.
R = (v₀² * sin(2θ)) / g
Variables:
- R is the range of the catapult
- v₀ is the initial velocity
- θ is the launch angle in degrees
- g is the acceleration due to gravity (approximately 9.81 m/s²)
To calculate the range, square the initial velocity, multiply by the sine of twice the launch angle, and then divide by the acceleration due to gravity.
What is a Catapult?
A catapult is a ballistic device used to launch a projectile a great distance without the aid of explosive devices—particularly various types of ancient and medieval siege engines. The catapult has been used since ancient times and is one of the most effective mechanisms during warfare. The mechanism works by storing potential energy in a tensioned arm or a twisted rope, which is then rapidly released to propel the projectile. The range and accuracy of a catapult depend on several factors, including the initial velocity, launch angle, and the acceleration due to gravity.
How to Calculate Catapult Range?
The following steps outline how to calculate the range of a catapult.
- First, determine the initial velocity (v₀).
- Next, determine the launch angle (θ).
- Next, determine the acceleration due to gravity (g).
- Finally, calculate the range using the formula R = (v₀² * sin(2θ)) / g.
- After inserting the values and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Initial Velocity (v₀) = 20 m/s
Launch Angle (θ) = 45 degrees
Acceleration due to Gravity (g) = 9.81 m/s²