Question

The picture below shows a roller coaster on a track where friction is negligible.
What is the ranking of the speeds at the indicated locations from highest speed to lowest speed?
Assume the roller coaster has enough speed at the beginning to make it through the entire trip

• A. $1,2,3,4$
• B. $4,3,2,1$
• C. $3,2,1,4$
• D. $4,1,2,3$
• E. $2,1,3,4$

Answer 1

Answer: (D)

$4,1,2,3$

From conservation of energy of the system, the total energy of the roller coaster remains the same.

Hence gravitational potential energy+Kinetic Potential Energy=constant.

$⟹mgh+\frac{1}{2}m{v}^2=constant$
$⟹v=\sqrt{\frac{2}{m}(constant-mgh)}$
Hence lower the height, higher the speed.

Thus the correct order is as given in the option D.