SOLUTION: a ball is thrown so that it starts out horizontally. it drops 0.3 m in going and 3 m horizontally. (a) how far does it drop in going 6 m horizontally? (2) how far horizontally does

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a ball is thrown so that it starts out horizontally. it drops 0.3 m in going and 3 m horizontally. (a) how far does it drop in going 6 m horizontally? (2) how far horizontally does      Log On


   

Question 571501: a ball is thrown so that it starts out horizontally. it drops 0.3 m in going and 3 m horizontally. (a) how far does it drop in going 6 m horizontally? (2) how far horizontally does it go in dropping 2.5 m?
Answer by KMST(5397) About Me  (Show Source):
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Physics textbooks show that the trajectory of a ball that rolls of a table is a parabola with drop proportional to the square of the horizontal distance.
Let x be the horizontal distance covered as the ball is dropping (in m).
Let y be the drop distance (in m).
y=kx%5E2
Substituting y=0.3 and x=3
0.3=k%2A3%5E2 --> 0.3=9k --> k=0.3%2F9 --> k=1%2F30
(a) for x=6, y=%281%2F30%296%5E2 --> y=36%2F30 --> y=1.2
The ball drops 1.2 m as it moves 6 m horizontally.
(b) for y=2.5 2.5=%281%2F30%29x%5E2 --> x%5E2=30%2A2.5 --> x%5E2=75 --> x=5sqrt%283%29 = approximately 8.7
The ball has moved 8.7 m horizontally as it dropped 2.5 m.