document.write( "Question 79829: A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. When will the ball reach a height of 80 m? \n" ); document.write( "

Algebra.Com's Answer #57288 by Earlsdon(6294) $\"\"$ $\"About$

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The height (as a function of time) of an object propelled upward from an initial height of $\"h%5B0%5D\"$ with an initial velocity of $\"v%5B0%5D\"$ is given by:
\n" ); document.write( " $\"h%28t%29+=+-4.9t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"$
\n" ); document.write( "In your problem:
\n" ); document.write( " $\"v%5B0%5D+=+20\"$ m/s
\n" ); document.write( " $\"h%5B0%5D+=+100\"$ m
\n" ); document.write( "You want to find at what value of t (time) will h (height) be 80 m. So, in the formula, you would set h(t) = 80 and solve for t.
\n" ); document.write( " $\"80+=+-4.9t%5E2%2B20t%2B100\"$ Subtract 80 from both sides.
\n" ); document.write( " $\"-4.9t%5E2%2B20t%2B20+=+0\"$ Solve for t using the quadratic formula: $\"t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ where:
\n" ); document.write( " $\"a+=+-4.9\"$
\n" ); document.write( " $\"b+=+20\"$
\n" ); document.write( " $\"c+=+20\"$ Making the appropriate substitutions, you'll get:
\n" ); document.write( " $\"t+=+%28-20%2B-sqrt%28%2820%29%5E2-4%28-4.9%29%2820%29%29%29%2F2%28-4.9%29\"$
\n" ); document.write( " $\"t+=+%28-20%2B-sqrt%28400%2B392%29%29%2F-9.8\"$
\n" ); document.write( " $\"t+=+%28-20%2B-sqrt%28792%29%29%2F%28-9.8%29\"$
\n" ); document.write( " $\"t+=+%28-20%2F%28-9.8%29%29%2B28.14%2F%28-9.8%29\"$ or $\"t+=+%28-20%2F%28-9.8%29%29-28.14%2F%28-9.8%29\"$
\n" ); document.write( " $\"t+=+-0.831\"$ or $\"t+=+4.913\"$ Discard the negative solution and keep the positive one.
\n" ); document.write( "The ball will reach a height of 80 meters about 4.9 seconds. \n" ); document.write( "

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