This is the correct equation for centripetal acceleration—acceleration towards the center of motion. in this case it isn't necessary to introduce a numerical factor. such a factor is often displayed explicitly as a constant k in front of the right-hand side; for example, a = kv2/r. as it turns out, k = 1 gives the correct expression. a good technique sometimes introduced in calculus-based textbooks involves using unknown powers of the dimensions. this problem would then be set up as [a] = [v]b[r]c. writing out the dimensions and equating powers of each dimension on both sides of the equation would result in b = 2 and c = −1.

Abasketball star covers 2.65 m horizontally in a jump to dunk the ball. his motion through space can be modeled precisely as that of a particle at his center of mass. his center of mass is at elevation 1.02 m when he leaves the floor. it reaches a maximum height of 1.90 m above the floor and is at elevation 0.910 m when he touches down again. (a) determine his time of flight (his "hang time"). (b) determine his horizontal velocity at the instant of takeoff. (c) determine his vertical velocity at the instant of takeoff. (d) determine his takeoff angle. (e) for comparison, determine the hang time of a whitetail deer making a jump with center-of-mass elevations yi = 1.20 m, ymax = 2.45 m, and yf = 0.750 m.