Projectile motion toy cannon problem

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SUMMARY

The projectile motion of a cannonball launched from a ramp at an angle involves calculating the range R along the ramp using the formula R = 2v^2_{0}cos^2θ_0(tanθ_0 - tanφ_0)/gcosφ_0. The discussion highlights the importance of aligning the coordinate axes with the ramp to accurately account for gravitational effects. Participants emphasize the necessity of providing all calculations and relevant equations to validate attempts at solving the problem.

PREREQUISITES
  • Understanding of projectile motion principles
  • Familiarity with trigonometric functions (sine, cosine, tangent)
  • Knowledge of kinematic equations, particularly for vertical motion
  • Ability to manipulate equations involving multiple variables
NEXT STEPS
  • Study the derivation of the projectile motion equations in inclined planes
  • Learn about the effects of angle and initial velocity on projectile range
  • Explore the concept of coordinate transformations in physics problems
  • Investigate the role of gravitational components in angled projectile motion
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Students studying physics, particularly those focusing on mechanics and projectile motion, as well as educators seeking to enhance their teaching methods in related topics.

ILoveOranges
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Homework Statement



a toy cannon is placed on a ramp that has a slope of angle beta. if the cannonball is projected up the hill at an angle of theta above the horizontal and has a muzzle speed of V, show that the range R of the cannonball (as measured along the ramp) is given by:



Homework Equations



R= [tex]2v^2_{0}cos^2\theta_0(tan\theta_0-tan\phi_0)/gcos\phi_0[/tex]

The Attempt at a Solution



i tried setting the x and y axes to match the ramp. this would make gravity acting on the cannon ball = [tex]cos\theta_0[/tex] . then i plugged that into y= [tex]\frac{1}{2} gt^2[/tex]. but since the y final does not end at 0, i didn't know what to do from there. is there a way to find the y final on the ramp??
 
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Hi ILoveOranges, welcome to PF.
To check your calculations you have to post all your attempts.
You have to post the relevant equations.
 

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