Max Range of Projectile on Non-Level Ground

Click For Summary
SUMMARY

The discussion focuses on deriving an equation to calculate the maximum range of a projectile on non-level ground. The key approach involves substituting the equations for vertical and horizontal components, y=R sin(α) and x=R cos(α), into the parabolic equation governing projectile motion. The range is determined as a function of the launch angle (θ), with the turning point identified by setting the derivative to zero. This method provides a structured way to analyze projectile motion in varying terrain.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with trigonometric functions and their applications
  • Knowledge of calculus, specifically derivatives
  • Ability to interpret and manipulate equations
NEXT STEPS
  • Study the derivation of projectile motion equations on inclined planes
  • Learn about optimization techniques in calculus
  • Explore the effects of varying launch angles on projectile range
  • Investigate numerical methods for solving complex projectile motion problems
USEFUL FOR

Students of physics, engineers working on projectile design, and anyone interested in advanced mechanics and optimization in motion analysis.

tman1
Messages
9
Reaction score
0
My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
 
Physics news on Phys.org
tman1 said:
My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
I think the best thing you can do is post whatever you have done. I could suggest a lot but I don't know what is making you go wrong.

The Bob (2004 ©)
 
Substitute
[tex]y=R\ sin\alpha[/tex]
and
[tex]x=R\ cos\alpha[/tex]
in the parabolic equation for the projectile.
The range will then be a function of [itex]\theta[/itex].The turning point of a function occurs where the derivative is zero...
 
Last edited:

Similar threads

Replies
40
Views
3K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 15 ·
Replies
15
Views
27K
Replies
23
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
Replies
4
Views
2K
Replies
1
Views
3K