Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve? A) v/2
B) v /√ 2
C) 2v
D) v√2

I shall answer it here because is coded horribly.

First, FN = mg/cos
On a banked curve, FNx is the only acceleration force
FNx = mv^2/r
FNx = FNsin
mg/cos * sin = mv^2/r
cancel out the mass (m) and sin*1/cos is tan
gtan = v^2/r
rgtan = v^2
√(rgtan) = v (this is the velocity for the smaller radius.)
call larger radius velocity X

for larger radius, it becomes 2r, so √(2rgtan) = X

understand you can do √xy = √x * √y

√(rgtan) * √2 = X (√(rgtan) = v)
v * √2 = X (where X is velocity with larger radius)

I hate how all of these newer answers do not break down the mechanics, understand using harder to grasp mechanics only makes it harder for the audience. You aren't cool for sounding smarter.

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