What is the Designed Speed for a 100 m Radius Curve Banked at 68 Degrees?

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The discussion revolves around calculating the designed speed for a banked curve with a 100 m radius and a 68-degree angle. The formula used is tan(angle) = v^2/(r*g), where g is the acceleration due to gravity. A participant initially miscalculated the speed due to using radians instead of degrees, leading to an incorrect result. The correct speed is approximately 49.25 m/s, derived from the formula v = √(rg*tan(68°)). The conversation highlights the importance of using the correct angle measurement in physics calculations.
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EASY speed of curve PROBLEM!

A race track curve has a radius of 100 m and is banked at an angle of 68 degrees. For what speed was the curve designed?


ok this is what i got

since tan angle = v^2/rg
i got tan 68 = v^2/rg
so tan 68 x rg = v^2
but this gave me an answer far from the actual answer of 49.
please help!
 
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v=\sqrt{980\tan68^\circ}\approx49.25:wink:
 
haha i had the calculator on radians
thank you haha
 
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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