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xzibition8612
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Homework Statement
A baseball slugger connects with a pitch 4 ft above the ground. The ball heads toward the 10-ft-high center-field fence, 455 ft away. The ball leaves the bat with a velocity of 125 ft/s and a slope of 3 vertical to 4 horizontal. Neglecting air resistance, determine whether the ball hits the fence (if it does, how high above the ground?) or whether it is a home run (if it is, by how much does it clear the fence?).
Homework Equations
F=ma (Euler form)
The Attempt at a Solution
The book gives the answer as home run, clears fence by 2 ft.
-mgj = m[ x2i+y2j+z2k) Note that i,j,k are unit vectors, and x2, y2, and z2 means double dot or acceleration.
-g = y2
0 = x2
y1 = -gt + C [C=125*(3/5)] => y1 = -gt + 75 (y1 is y dot or velocity)
y = (-gt^2)/2 + 75t + C [C=4] => y = -(gt^2)/2+75t+4
x1 = C [C=125*(4/5)] => x1 = 100
x = 100t + C [C=0 because no movement in x direction at t = 0] = > x=100t
Got these equations, then plugged in 455 ft into x=100t to get t=4.55s. So at 4.55s the ball would reach the fence. As to how high it will be, plug t=4.55 into the y equation, and my answer is 243 ft. The fence is 10 ft, so it clears it by 233 ft. But the book's answer is 2 ft. I know I screwed up somewhere, but I can't see it. Any help would be appreciated.
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