6) A pitcher is employing a ballistic pendulum to determine the speed of his fastball. A 3.3 kg lump of clay is suspended from a cord 2.0 m long. When the pitcher throws his fastball aimed at the clay, the ball becomes embedded in the clay and the two swing up to a maximum height of 0.08 m. If the mass of the baseball is 0.21 kg, find the speed of the pitch.

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)