During the Boston Red Sox\' history-making comeback in the 7thgame of the 2004 A

Question

During the Boston Red Sox' history-making comeback in the 7thgame of the 2004 ACLS against the New York Yankees, Manny Ramirezhits a pitched ball from Mariano Rivera. Th eball is hit at aheight of 4 feet above the ground so that its angle of projectionis 45 degree and its initial speed is 106 ft/sec. the ball is hitdown the left field line where a 37 foot fence (called the GreenMonster) is located 310 feet from home plate. (keep in mindthat "g" will not be 9.8 m/s^2 in this problem because youare using feet. rather than meters... it will be 32 ft/s^2). A. Will Manny's hit clear the green Monster? show yourwork B. At the time the ball either clears or hits the Greenmonster, how fast (its speed) is it going. During the Boston Red Sox' history-making comeback in the 7thgame of the 2004 ACLS against the New York Yankees, Manny Ramirezhits a pitched ball from Mariano Rivera. Th eball is hit at aheight of 4 feet above the ground so that its angle of projectionis 45 degree and its initial speed is 106 ft/sec. the ball is hitdown the left field line where a 37 foot fence (called the GreenMonster) is located 310 feet from home plate. (keep in mindthat "g" will not be 9.8 m/s^2 in this problem because youare using feet. rather than meters... it will be 32 ft/s^2). A. Will Manny's hit clear the green Monster? show yourwork B. At the time the ball either clears or hits the Greenmonster, how fast (its speed) is it going.

Explanation / Answer

initial horizontal velocity=106*cos45 horizontal displacement=310 horizontal acceleration=0 time taken to travel 310 m=t 310=106*cos45*t t=4.14 s initial vertical velocity=106*sin45 vertical acceleration=g=32 let time taken to reach maximum height=T v=u-g*T 0=106*sin45-32*T T=2.34 s maximum height reached by the ball=H v2=u2-2*g*H 0=(106*sin45)2-2*32*H H=87.78 in (4.14-2.34)=1.8 s the ball fell h m from the highest point u=0 h=u*t+(1/2)*g*t2 h=0+(1/2)*32*1.82 h=51.84 let after 1.8 s it's velocity=V V=u+g*1.8 V=0+32*1.8 V=57.6 ft/s so after traveling 310 ft horizontally the ball is (87.78-51.84)ftor 35.94 above the point from where it was hit the ball is 35.94+4=39.94 ft above the ground so it easilyclear the green monster when the ball clear green monster it's vertical velocity=57.6 ft/sand it's horizontal velocity=106*cos45=74.95 ft/s speed the ball had when it clears the greenmonster=(57.62+74.952)=94.53 ft/s

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