Chapter 12.6, Problem 64ES

As illustrated in the accompanying figure, a train is traveling on a curved track. At a point where the train is traveling at a speed of $132\text{ft}/\text{s}$ and the radius of curvature of the track is 3000 ft, the engineer hits the brakes to make the train slow down at a constant rate of $7.5\text{ft}/{\text{s}}^{\text{2}}.$

(a) Find the magnitude of the acceleration vector at the instant the engineer hits the brakes.

(b) Approximate the angle between the acceleration vector and the unit tangent vector T at the instant the engineer hits the brakes.