Answer to Question #605 in Mechanics | Relativity for jfdak

Question #605
A baseball being hit is in contact with the bat for 1.30 ms. The ball is moving toward the bat at speed 38.0 m/s just before it is hit, and is moving at 67.5 m/s away from the bat just after it is hit. Assume the ball has a constant acceleration while it is in contact with the bat, and that the ball&rsquo;s motion is always along a straight line. (a)Calculate the acceleration of the ball while it is being hit. (b)What is the ball&rsquo;s net displacement while it is in contact with the bat?
a)Constant acceleration a reduces initial velocity and increases inverse velocity for t = 1.3*10&macr;&sup3; s. General change of velocity is
&Delta;&nu;=(38+67.5) m/s, hence:
&Delta;&nu;=at
a=&Delta;&nu;/t=((38+67.5)m/s)/1.3*10&macr;&sup3;s&asymp;81.154*10&sup3; m/s&sup2;
b)Ball&rsquo;s net displacement is:
&Delta;x=(&nu;&omicron;*t)+(at&sup2;)/2=38m/s*1.3*10&macr;&sup3;s+(81.154*10&sup3; m/s&sup2;*(1.3*10&macr;&sup3;s)&sup2;/2)&asymp;0.118m=11.8cm

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