Question

A small roller coaster start at point A with a speed is on a curved track as shown in the figure. Consider the friction between the roller coaster and the track to be negligible. Also the coaster always remains in contact with the track. The speed of roller coaster at point D on the track under the given conditions must have been

• A. $\left(u^{2} + g h\right)^{1 / 2}$
• B. $\left(u^{2} + 2 g h\right)^{1 / 2}$
• C. $\left(u^{2} + 4 g h\right)^{1 / 2}$
• D. $u$

Answer 1

Answer: (C)

Let the speed of the roller coaster at point D be v.
Applying the law of conservation of energy between point A and D, we get
$\frac{1}{2}mu^{2}+mg\left(2 h\right)=\frac{1}{2}mv^{2}+0$
$or \, u^{2}+4gh=v^{2} \, or \, v=\sqrt{u^{2} + 4 g h \, }$