document.write( "Question 1161488: A roller-coaster car shown below is pulled up to point 1 where it is released from rest. Assumiming no friction. Calculate the speed at points 2, 3, and 4.\r
\n" ); document.write( "\n" ); document.write( "Height 1=32m
\n" ); document.write( "Height 2= 0
\n" ); document.write( "Height 3= 26 m
\n" ); document.write( "Height 4= 14 m \n" ); document.write( "

Algebra.Com's Answer #785065 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"v%5B1%5D\"$ , $\"v%5B2%5D\"$ , $\"v%5B3%5D\"$ , and $\"v%5B4%5D\"$ be the velocities of roller coaster at different points, and $\"h%5B1%5D\"$ , $\"+h%5B2%5D\"$ , $\"h%5B3%5D\"$ , and $\"h%5B4%5D\"$ be the height of the points respectively.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Write the given values of question.\r
\n" ); document.write( "\n" ); document.write( " $\"h%5B1%5D=32m\"$
\n" ); document.write( " $\"h%5B2%5D=0\"$
\n" ); document.write( " $\"h%5B3%5D=26m\"$
\n" ); document.write( " $\"h%5B4%5D=14m\"$ \r
\n" ); document.write( "\n" ); document.write( "we know start is at point $\"h%5B1%5D\"$ , so $\"highlight%28v%5B1%5D=0%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Write the expression for conservation of energy between points 1 and 2 and substitute the above values.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"K%2AE%5B1%5D%2BP%2AE%5B1%5D=K%2AE%5B2%5D%2BP%2AE%5B2%5D\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0%2Bmgh%5B1%5D=%281%2F2%29mv%5B2%5D%5E2%2B0\"$ ...........simplify\r
\n" ); document.write( "\n" ); document.write( " $\"gh%5B1%5D=%281%2F2%29v%5B2%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B2%5D%5E2=gh%5B1%5D%2F%281%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B2%5D%5E2=2gh%5B1%5D\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B2%5D=sqrt%282gh%5B1%5D%29\"$ ........plug in $\"g=9.81%28m%2Fs%5E2%29\"$ and $\"h%5B1%5D=32m\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B2%5D=sqrt%282%2A9.81%28m%2Fs%5E2%29%2A32m%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B2%5D=sqrt%28%28627.84m%5E2%29%2Fs%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28v%5B2%5D=25.0567%28m%2Fs%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"K%2AE%5B2%5D%2BP%2AE%5B2%5D=K%2AE%5B3%5D%2BP%2AE%5B3%5D\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29mv%5B2%5D%5E2%2Bmgh%5B2%5D=%281%2F2%29mv%5B3%5D%5E2%2Bmgh%5B3%5D\"$ ....simplify and substitute known\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( " $\"%28313.919m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2%2B%28255.06m%5E2%29%2Fs%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28313.919m%5E2%29%2Fs%5E2-%28255.06m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%2858.859m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B3%5D%5E2=%2858.859m%5E2%2Fs%5E2%29%2F%281%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B3%5D%5E2=%28117.718m%5E2%29%2Fs%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B3%5D=sqrt%28%28117.718m%5E2%29%2Fs%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28v%5B3%5D=10.8498%28m%2Fs%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"K%2AE%5B3%5D%2BP%2AE%5B3%5D=K%2AE%5B4%5D%2BP%2AE%5B4%5D\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29mv%5B3%5D%5E2%2Bmgh%5B3%5D=%281%2F2%29mv%5B4%5D%5E2%2Bmgh%5B4%5D\"$ ....simplify \r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29v%5B3%5D%5E2%2Bgh%5B3%5D=%281%2F2%29v%5B4%5D%5E2%2Bgh%5B4%5D\"$ ......substitute known\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( " $\"%28313.919m%5E2%29%2Fs%5E2-+%28137.34m%5E2%29%2Fs%5E2+=%281%2F2%29v%5B4%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28176.579m%5E2%29%2Fs%5E2=%281%2F2%29v%5B4%5D%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B4%5D%5E2=%28176.579m%5E2%2Fs%5E2%29%2F%281%2F2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B4%5D%5E2=%28353.158m%5E2%29%2Fs%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"v%5B4%5D=sqrt%28%28353.158m%5E2%29%2Fs%5E2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"highlight%28v%5B4%5D=18.7925%28m%2Fs%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );