document.write( "Question 1072666: Peter is standing on a bridge and throws a stone up into the air at 30 m/s. The stone hits the surface of the water below 10 seconds later. From what height above the surface of the water did Peter throw the stone? (Note: the acceleration due to gravity is 10 m/s^2 ) \n" ); document.write( "

Algebra.Com's Answer #687496 by KMST(5328) $\"\"$ $\"About$

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WITHOUT FORMULAS:
\n" ); document.write( "The initial upwards speed was $\"%2230+m+%2Fs%22\"$ .
\n" ); document.write( "For $\"10s\"$ , that upwards speed decreased linearly due to gravity
\n" ); document.write( "by $\"%2210+m+%2Fs%22\"$ each $\"s\"$ $\"%22%28+10%22\"$ $\"m\"$ $\"%22%2F%22\"$ $\"s%5E2\"$ $\"%22%29%22\"$ ,
\n" ); document.write( "for a total decrease of $\"10%2A10\"$ $\"%22m+%2Fs%22+=+100\"$ $\"%22m+%2Fs%22\"$
\n" ); document.write( "to $\"%2230+m+%2Fs%22-%22100+m+%2Fs%22=%22-+70+m+%2Fs%22\"$ .
\n" ); document.write( "The average upwards speed for those $\"10s\"$ was
\n" ); document.write( " $\"%2830%2B%28-70%29%29%2F2\"$ $\"%22m+%2Fs%22+=+-20\"$ $\"%22m+%2Fs%22\"$ .
\n" ); document.write( "At an average speed of $\"-20\"$ $\"%22m+%2Fs%22\"$ for $\"10s\"$ ,
\n" ); document.write( "the stone's upwards displacement was
\n" ); document.write( " $\"%2810s%29\"$ $\"%22%28-20+m+%2F+s+%29+=+-200+m%22\"$
\n" ); document.write( "So, the stone left Peter's hand $\"highlight%28200m%29\"$ above the surface of the water.
\n" ); document.write( "
\n" ); document.write( "WITH FORMULAS:
\n" ); document.write( "You may have learned in physics class that, for an object moving linearly under constant acceleration,
\n" ); document.write( "its position $\"%28x%29\"$ as a function of time $\"%28t%29\"$ can be modeled as
\n" ); document.write( " $\"x%28t%29=x%5B0%5D%2Bv%5B0%5Dt%2B%281%2F2%29at%5E2\"$ , where
\n" ); document.write( " $\"a\"$ is the constant acceleration, while
\n" ); document.write( " $\"x%5B0%5D\"$ and $\"v%5B0%5D\"$ are respectively the position and velocity of the object at $\"t=0\"$ .
\n" ); document.write( "You could choose to measure position as height (in meters) above the water surface,
\n" ); document.write( "and time (in seconds) since the stone left Peter's hand.
\n" ); document.write( "In that case, distance above the water, upwards velocity and upwards acceleration are positive,
\n" ); document.write( "so initial velocity is $\"v%5B0%5D=30\"$ $\"%22%28+m+%2F+s+%29%22\"$ ,
\n" ); document.write( "acceleration is $\"a=-10\"$ $\"%22%28+m+%2F%22\"$ $\"s%5E2\"$ $\"%22%29%22\"$ ,
\n" ); document.write( " $\"x%5B0%5D\"$ is what you are looking for ,
\n" ); document.write( "and you know that $\"x%2810%29=0\"$ at $\"t=10\"$ .
\n" ); document.write( "Substituting into $\"x%28t%29%2Bx%5B0%5D%2Bv%5B0%5Dt%2B%281%2F2%29at%5E2\"$ ,
\n" ); document.write( " $\"x%2810%29=x%5B0%5D%2B30%2A10%2B%281%2F2%29%28-10%29%2A10%5E2\"$ ,
\n" ); document.write( " $\"0=x%5B0%5D%2B300-5%2A100\"$ ,
\n" ); document.write( " $\"0=x%5B0%5D-200\"$ , and $\"x%5B0%5D=highlight%28200%29\"$ (in meters , of course). \n" ); document.write( "

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