SOLUTION: 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. Height 1=32m Height

Algebra ->  Test -> SOLUTION: 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. Height 1=32m Height      Log On


   

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.
Height 1=32m
Height 2= 0
Height 3= 26 m
Height 4= 14 m
Answer by MathLover1(20850) About Me  (Show Source):
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.

Write the given values of question.
h%5B1%5D=32m
h%5B2%5D=0
h%5B3%5D=26m
h%5B4%5D=14m
we know start is at point h%5B1%5D, so highlight%28v%5B1%5D=0%29
Write the expression for conservation of energy between points 1 and 2 and substitute the above values.

K%2AE%5B1%5D%2BP%2AE%5B1%5D=K%2AE%5B2%5D%2BP%2AE%5B2%5D
0%2Bmgh%5B1%5D=%281%2F2%29mv%5B2%5D%5E2%2B0...........simplify
gh%5B1%5D=%281%2F2%29v%5B2%5D%5E2
v%5B2%5D%5E2=gh%5B1%5D%2F%281%2F2%29
v%5B2%5D%5E2=2gh%5B1%5D
v%5B2%5D=sqrt%282gh%5B1%5D%29........plug in g=9.81%28m%2Fs%5E2%29 and h%5B1%5D=32m
v%5B2%5D=sqrt%282%2A9.81%28m%2Fs%5E2%29%2A32m%29
v%5B2%5D=sqrt%28%28627.84m%5E2%29%2Fs%5E2%29
highlight%28v%5B2%5D=25.0567%28m%2Fs%29%29


K%2AE%5B2%5D%2BP%2AE%5B2%5D=K%2AE%5B3%5D%2BP%2AE%5B3%5D
%281%2F2%29mv%5B2%5D%5E2%2Bmgh%5B2%5D=%281%2F2%29mv%5B3%5D%5E2%2Bmgh%5B3%5D....simplify and substitute known

%28313.919m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2%2B%28255.06m%5E2%29%2Fs%5E2
%28313.919m%5E2%29%2Fs%5E2-%28255.06m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2
%2858.859m%5E2%29%2Fs%5E2=%281%2F2%29v%5B3%5D%5E2
v%5B3%5D%5E2=%2858.859m%5E2%2Fs%5E2%29%2F%281%2F2%29
v%5B3%5D%5E2=%28117.718m%5E2%29%2Fs%5E2
v%5B3%5D=sqrt%28%28117.718m%5E2%29%2Fs%5E2%29
highlight%28v%5B3%5D=10.8498%28m%2Fs%29%29


K%2AE%5B3%5D%2BP%2AE%5B3%5D=K%2AE%5B4%5D%2BP%2AE%5B4%5D
%281%2F2%29mv%5B3%5D%5E2%2Bmgh%5B3%5D=%281%2F2%29mv%5B4%5D%5E2%2Bmgh%5B4%5D....simplify
%281%2F2%29v%5B3%5D%5E2%2Bgh%5B3%5D=%281%2F2%29v%5B4%5D%5E2%2Bgh%5B4%5D......substitute known

%28313.919m%5E2%29%2Fs%5E2-+%28137.34m%5E2%29%2Fs%5E2+=%281%2F2%29v%5B4%5D%5E2
%28176.579m%5E2%29%2Fs%5E2=%281%2F2%29v%5B4%5D%5E2
v%5B4%5D%5E2=%28176.579m%5E2%2Fs%5E2%29%2F%281%2F2%29
v%5B4%5D%5E2=%28353.158m%5E2%29%2Fs%5E2
v%5B4%5D=sqrt%28%28353.158m%5E2%29%2Fs%5E2%29
highlight%28v%5B4%5D=18.7925%28m%2Fs%29%29