Finding Acceleration on 30° Downward Slope w/ 0.10 Coeff. of Friction

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To find the acceleration of a runner on a 30° downward slope with a coefficient of kinetic friction of 0.10, the net force equation is essential. The participant initially uses the formula a = 9.81 x (0.5 - 0.10(0.866)) to calculate acceleration. There is curiosity about whether this is the only method or if there are alternative approaches to determine the net force. The discussion emphasizes the importance of understanding the components of forces acting on the runner, including gravitational and frictional forces. Exploring different methods to calculate acceleration can enhance comprehension of the underlying physics principles.
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Homework Statement



A person is running down a hill which is a 30° downward slope. If the coefficient of kinetic friction is 0.10, what is acceleration of the runner.

Homework Equations



Fnet=F┴-Ff


The Attempt at a Solution



Since we are only given 2 known things, the θ is 30° and the kinetic friction is 0.10. I am wondering if I am using the correct formula and need to be pointed in direction of what else to find to actually find the acceleration. I know we need Fnet but that is not all.
 
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Ok I have found out the answer one way by just doing a = 9.81 x (0.5-0.10(0.866)) but is there a different way to find the answer or is this the only one? I mean by finding Fnet and somehow answering it a different way?
 
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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