Finding the Angle of a Bowling Ball Ramp Problem

AI Thread Summary
To find the angle between the ramp and the floor, the problem involves a bowling ball traveling down an 8.5-meter ramp, taking approximately 5.0243 seconds to reach the bottom. Using the acceleration due to gravity, a = 9.81 m/s², the discussion emphasizes applying kinematic equations to derive the angle. Participants are encouraged to share their attempts and identify specific areas of difficulty for effective assistance. The focus is on collaboratively solving the problem through shared insights and calculations. Engaging with the community can lead to a clearer understanding of the physics involved.
mteykl
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Homework Statement



There is a bowling ball traveling down a ramp. The ball starts resting. The ramp's hypotenuse is 8.5 meters long and is across from a 90 degree angle. The average time it takes the ball to travel down the ramp is about 5.0243 seconds. We can assume a=9.81m/s^2. What is the angle horizontal made at the bottom of the ramp and the floor?

Homework Equations





The Attempt at a Solution

 
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welcome to pf!

hi mteykl! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
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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