For a short time the position of a roller-coaster car along its path is defined by the equations r = 25 m, = (0.3t) rad, and z = (-8 cos) m, where t is measured in seconds, Determine the magnitudes of the car's velocity and acceleration when t = 4s.

A package is dropped from the plane which is flying with a constant horizontal velocity of v_A = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just before it is released from plane at A.

If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B arises.

The motorcyclist attempts to jump over a series of cars and trucks and lands smoothly on the other ramp, i.e., such that his velocity is tangent to the ramp at B. Determine the launch speed v_A necessary to make the jump.

A car, initially at rest, moves along a straight road with constant acceleration such that it attains a velocity of 60 ft/s when s = 150 ft. Then after being subjected to another constant acceleration, it attains a final velocity of 100 ft/s when s = 325 ft. Determine the average velocity and average acceleration of the car for the entire 325-ft displacement.