document.write( "Question 30576: A circus clown at the top of a 60-foot platform is playing catch with another clown on the ground.
\n" ); document.write( "The clown on the platform drops a ball at the same time as the one on the ground tosses a ball upward at 80 ft/sec.
\n" ); document.write( "For what length of time is the distance between the balls less than or equal to 10 feet? Hint: the initial velocity of a ball that is dropped is 0 ft/sec. The formula for the height S in feet above the earth at a time t seconds for an object projected into the air with an initial velocity of v ft/sec from an initial height of s0 is:
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\n" ); document.write( "S = -16t2 + v0t + s0 \n" ); document.write( "
Algebra.Com's Answer #17273 by Fermat(136)\"\" \"About 
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There are two eqns of motion. One for the ball falling down. And one for the ball which is thrown upwards.
\n" ); document.write( "Let s1 represent the height of the dropped ball, above the ground
\n" ); document.write( "Let s2 represent the height of the thrown ball, above the ground.
\n" ); document.write( "Using the eqn of motion you have, S = -16t2 + v0t + s0, and substituting in appropriate values for s0 and v0, (upwards is taken as positive)
\n" ); document.write( "s1 = 60 - (1/2)gtē
\n" ); document.write( "s2 = 80t - (1/2)gtē
\n" ); document.write( "subtracting one height from t'other,
\n" ); document.write( "s1 - s2 = 60 - 80t
\n" ); document.write( "For the difference in height to be less than or equal to 10, we can write,
\n" ); document.write( "|s1 - s2| = |60 - 80t| <= 10
\n" ); document.write( "We therefore have two inequalities,
\n" ); document.write( "60 - 80t <= 10
\n" ); document.write( "and
\n" ); document.write( "80t - 60 <= 10
\n" ); document.write( "From the 1st inequality,
\n" ); document.write( "60 - 80t <= 10
\n" ); document.write( "60 - 10 <= 80t
\n" ); document.write( "80t >= 50
\n" ); document.write( "t >= 5/8
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\n" ); document.write( "From the 2nd inequality,
\n" ); document.write( "80t - 60 <= 10
\n" ); document.write( "80t <= 70
\n" ); document.write( "t <= 7/8
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\n" ); document.write( "The balls will be less than or equal to 10 feet apart in the time interval denoted by.
\n" ); document.write( "5/8 <= t <= 7/8
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