Calculating Maximum Range of a Catapulted Rock

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Homework Help Overview

The discussion revolves around calculating the maximum range of a rock launched by a catapult, specifically focusing on the relationship between the mass of the counterweight, the mass of the rock, and the height from which the counterweight falls.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to equate potential and kinetic energy to derive the maximum range formula. Some participants question the optimal launch angle for achieving maximum range, while others provide a specific angle of 45 degrees and inquire about the range at that angle with a given velocity.

Discussion Status

The discussion is active, with participants exploring different aspects of projectile motion and energy conservation. There is a mix of attempts to derive formulas and questions about specific conditions for maximum range.

Contextual Notes

Participants are working under the assumption that the rock is launched from ground level, and there may be constraints related to the parameters of the problem, such as the specific values of mass and height not being provided.

Gank
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Homework Statement


Assuming that the rock launched by a catapult is released from ground level, show that the theoretical maximum range is:
R=2Mh/m, where M = mass of counterweight
m = mass of rock
h = height counterweight falls


Homework Equations



Ep=mgh
Ek=(mv^2)/2

The Attempt at a Solution



I equated the two expressions and then split the velocity into its components so this splits the Ek up into horizontal and vertical but I can't progress from here
 
Physics news on Phys.org
At what angle should a projectile be launched to obtain a maximum range?
 
45degrees
 
What is the range when the angle is 45 degrees and the magnitude of velocity is some v?
 

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