Question

A baseball pitcher throws a ball with a speed of 41 m/s. Estimate the average acceleration of the ball during the throwing motion. In throwing the baseball, the pitcher accelerates the ball through a displacement of about 3.5 m, from behind the body to the point where it is released.

Answer 1

When t=0, v=0, d=0 When t=tf, v=41m/s, d=3.5m We have 2 formulas – the ones corresponding to uniformly accelerated linear movement: vf=a*t+vo d=(1/2)*a*t^2+vo*t Let’s put the data in the formulas: 41m/s=a*t+0=a*t 3.5m=(1/2)*a*t^2+0*t=1/2*a*t^2 You can use a variety of methods to find t and a. I will choose substitution. t=(41m/s)/a 3.5m=(1/2)*a*((41m/s)/a)^2=(1/2)*a*(41m/s)^2/a^2=(1/2)*(41m/s)^2/a a=(1/2)*(41m/s)^2/(3.5m)=(1/2)*41^2(m^2/s^2)/(3.5m) a=41^2(m/s^2)/( 2*3.5)=240m/s^2