Physics

Problem

A smooth roller-coaster track contains three marked points:

A

B

, and

C

, situated at heights of

30\,\text{m}

10\,\text{m}

, and

25\,\text{m}

, respectively, above the ground. A car of mass

200\,\text{kg}

is released from rest at

A

and allowed to move along the track. Air resistance is negligible unless otherwise stated. Take

g = 9.8\,\text{m}\,\text{s}^{-2}

. a. (i) Determine the speed of the car when it reaches point

B

. b. (ii) Calculate the speed of the car at point

C

assuming no energy losses. c. (iii) In reality,

5\%

of the mechanical energy possessed by the car at

A

is dissipated as thermal energy by the time it arrives at

C

. Recalculate the speed at

C

under this condition.