Projectile motion toy cannon problem

AI Thread Summary
The discussion revolves around solving a projectile motion problem involving a toy cannon on a ramp. The goal is to derive the range of the cannonball along the ramp using the given formula. A participant attempted to set the axes to align with the ramp and adjusted the gravity component accordingly but faced challenges with the final vertical position of the cannonball. The conversation emphasizes the importance of sharing all calculation attempts and relevant equations for effective problem-solving. Clear communication of the steps taken is crucial for receiving constructive feedback.
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= 2v^2_{0}cos^2\theta_0(tan\theta_0-tan\phi_0)/gcos\phi_0

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 = cos\theta_0 . then i plugged that into y= \frac{1}{2} gt^2. 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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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