Jo 13.1 A car drives through portion AB of the S-curve at constant speed. decelerates in BC, and accelerates in CD. Show the approximate direction of the acceleration vector at each of the five points indicated. 13.2 A car is driving around a curve of radius 200 m, while increasing its speed at the rate of 0.8 m/s. At a certain instant, the magnitude of the total acceleration is measured to be 1.5 m/s. What is the speed of the car at that instant measured in km/h? 13.3 The rocket is in powered flight close to the surface of the earth. Determine the radius of curvature of the path at the instant shown if the speed of the rocket is 800 ft/s. Note that the acceleration of the rocket has two components-the acceleration due to the thrust of the rocket engines and the acceleration due to gravity 13.4 The car is traveling at a constant speed through a dip in the road. The radius of curvature of the road at point A, the bottom of the dip, is 1500 ft. What speed of the car, measured in mi/h, would result in an acceleration of magnitude 0.25g when the car is at A? 13.5 A ball is shot from the cannon at A with the initial velocity v, directed at the angle with the horizontal. Derive the expression for the radius of curvature at B-the highest point on the path of the ball. Figure P13.1 300 BA Figure P13.3 1500 Figure P13.5 13.6 A particle travels along the circular path of radius R-2 ft, starting from rest at A and increasing its speed at a constant rate. When the particle reaches B, its speed is 5 ft/s. Determine the magnitude of the acceleration of the particle at B. 13.7 A particle moves along the path shown with a constant speed of 2 m/s. Determine the magnitude of the acceleration at points A, B, and C. 13.8 A particle moves along a plane curve from a point O to a point B. The path length between O and B is 80 in. The tangential component of the acceleration is Figure P13.4 R Figure P13.6 y (m) A B 4 cos x 0 x (m) 14 x12 Figure P13.7 TI-84 Plus C Silver Edition TEXAS INSTRUMENTS NORMAL FLOAT RUTO REAL DEGREE MP Ans-Ans 9