Finding Velocity via Convervation of Energy

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The discussion focuses on solving a projectile motion problem using the conservation of energy principle. The initial energy is calculated using the formula for kinetic energy and gravitational potential energy, while the final energy is expressed solely in terms of kinetic energy. A common mistake highlighted is the incorrect application of the initial velocity component in the calculations, as the problem should not involve 2D motion analysis. The correct approach is to use the initial velocity of 195 m/s directly in the energy equation. The final velocity when the projectile strikes the ground is derived from this corrected understanding of energy conservation.
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Homework Statement


A projectile is shot upward from the top of a cliff in an angle of 25 with a velocity of 195 m/s.The height of the cliff is 315m. What will be its speed when it strikes the ground below? (Use conservation of energy)



Homework Equations


Ok...initial energy = final energy

Initial energy = .5m*(initial velocity square) + mgy
Final energy = .5m*(final velocity square)

initial velocity = sin*theta*upward initial velocity = sin25*195


The Attempt at a Solution



So I set them to equal and I got final V to be 114, but it says I had it wrong, canceling out the mass... I have no clue what I did wrong there...
 
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initial velocity = sin*theta*upward initial velocity = sin25*195
should not be used in this one. It is an energy problem, not a 2D motion analysis. Just use the 195 in the first 1/2m*v^2.
 
Delphi51 said:
should not be used in this one. It is an energy problem, not a 2D motion analysis. Just use the 195 in the first 1/2m*v^2.

OK, thank you! =)
 
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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