# Engineering Dynamics: Normal-Tangential Components

1. Feb 12, 2012

### ben.tien

1. The problem statement, all variables and given/known data
A race boat is traveling at a constant speed v0 = 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 vf = 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(d2y/dx2))

*edit* an = v2

a = atut + anun

v = vut

at t = 0;
ut = -sin90i + cos90j
3. The attempt at a solution

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

converting mph to ft / s
v2 = v02 + 2 ac(s - s0)
[(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.

Last edited: Feb 12, 2012
2. Feb 12, 2012

### PhanthomJay

The equation you have written assumes tangential acceleration only at -1g. You want the total resultant acceleration (centripetal plus tangential, vectorially added) not to exceed 2g's.