The roller coaster speed when it reaches to ground level is 15.65 m/sec
Given-
Roller coaster is released at a height of 125 meters.
It is known that, square of the final velocity [tex]v[/tex] of the body is equal to the sum of the square of initial velocity [tex]v_{10}[/tex] and the product of the twice of acceleration [tex]a[/tex] and displacement [tex]d[/tex]. It can be written as,
[tex]v^{2} =v_{0}^2+2ad[/tex]
Roller coaster released from rest therefore initial velocity is zero.
[tex]v^{2} =0+2ad[/tex]
[tex]v^{2} =2ad[/tex]
Roller coaster will fall towards the ground with an acceleration equal to gravity g and height of 125 m. therefore,
[tex]v^{2} =2\times g\times 125[/tex]
[tex]v^{2} =2\times 9.8\times 125[/tex]
[tex]v^{2} =2450[/tex]
[tex]v=15.65[/tex]
Hence, the roller coaster speed when it reaches to ground level is 15.65 m/sec.
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