(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A race boat is traveling at a constant speed v_{0}= 130 mph when it performs a turn with constant radius ρ to change its course by 90°. The turn is performed while losing speed uniformly in time so that the boat's speed at the end of the turn is v_{f}= 116 mph. If the magnitude of the acceleration is not allowed to exceed 2g, where g is the acceleration due to gravity, determine the tightest radius of curvature possible and the time needed to complete the turn.

2. Relevant equations

ρ(x) = ([1 + (dy/dx)^{2}]^{3/2})/(absvalue(d^{2}y/dx^{2}))

*edit* a_{n}= v^{2}/ρ

a= a_{t}u_{t}+ a_{n}u_{n}

v= vu_{t}

at t = 0;

u_{t}= -sin90i+ cos90j

3. The attempt at a solution

So the distance traveled by the boat is 1/4 of a circle, s = rθ = ρ([itex]\pi[/itex]/2)

converting mph to ft / s

v^{2}= v_{0}^{2}+ 2 a_{c}(s - s_{0})

[(170.13)^{2}- (190.67)^{2}] / 2(32.2 ft/ s ^2) = s

s = 57.5 ft = 17.5 meters

ρ = 57.5 ft * 2 / pi

I feel like I'm missing something BIG because it can't be this simple.

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# Homework Help: Engineering Dynamics: Normal-Tangential Components

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