(The spin of a baseball) When a ball is thrown with spin abo

Question and Solution

(The spin of a baseball) When a ball is thrown with spin about an axis that is not parallel to its velocity, it experien

98 % (455 Review)

(The spin of a baseball) When a ball is thrown with spin about an axis that is not parallel to its velocity, it experiences a lateral acceleration due to differences in friction along its sides. This spin acceleration is given by as D kS v, where v is the velocity of the ball, S is the angular velocity of its spin, and k is a positive constant depending on the surface of the ball. Suppose that a ball for which k D 0:001 is thrown horizontally along the x-axis with an initial speed of 70 ft/s and a spin of 1,000 radians/s about a vertical axis. Its velocity v must satisfy 8 < : dv dt D .0:001/.1;000k/ v ? 32k D k v ? 32k v.0/ D 70i; since the acceleration of gravity is 32 ft/s2. (a) Show that the components of v D v1i C v2j C v3k satisfy 8 < : dv1 dt D ?v2 v1.0/ D 70 8 < : dv2 dt D v1 v2.0/ D 0 8 < : dv3 dt D ?32 v3.0/ D 0. (b) Solve these equations, and find the position of the ball t s after it is thrown. Assume that it is thrown from the origin at time t D 0. (c) At t D 1=5 s, how far, and in what direction, has the ball deviated from the parabolic path it would have followed if it had been thrown without spin?

Disclaimer: Crazy For Study provides academic assistance to students so that they can complete their college assignments and projects on time. We strictly do not deliver the reference papers. This is just to make you understand and used for the analysis and reference purposes only.