Calculating Maximum Range of a Catapulted Rock

Click For Summary
The discussion focuses on deriving the theoretical maximum range of a rock launched from a catapult, expressed as R=2Mh/m, where M is the mass of the counterweight, m is the mass of the rock, and h is the height from which the counterweight falls. Participants explore the relationship between potential energy (Ep) and kinetic energy (Ek) to establish this formula. The optimal launch angle for achieving maximum range is identified as 45 degrees. Additionally, there is inquiry into calculating the range when the launch angle is 45 degrees and the velocity is a variable v. The conversation emphasizes the physics principles governing projectile motion and energy conversion in catapult mechanics.
Gank
Messages
31
Reaction score
0

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?
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Catapult Shooting Distance: 76.79m
  • · Replies 4 ·
Replies
4
Views
2K
Calculating the Velocity of a Catapulted Object
  • · Replies 5 ·
Replies
5
Views
2K
Catapult spring, Kinetic and Potential energy
  • · Replies 10 ·
Replies
10
Views
3K
Projectile Motion Kinematics: A catapult launches a rock....
  • · Replies 5 ·
Replies
5
Views
4K
Why is my calculation for a rocket's maximum range incorrect?
  • · Replies 21 ·
Replies
21
Views
3K
Maximum speed of a cylinder dropped on a spring
  • · Replies 4 ·
Replies
4
Views
2K
How can the momentum of a thrown rock be calculated with given parameters?
  • · Replies 1 ·
Replies
1
Views
1K
Calculating Launch Speed for a Catapult with Drag Force
  • · Replies 5 ·
Replies
5
Views
1K
Calculating the Distance a Rock Travels Up a Sloped Hill
  • · Replies 7 ·
Replies
7
Views
1K
Projectile motion -- Maximum range it can travel inside a 2m tunnel
  • · Replies 4 ·
Replies
4
Views
2K