Question

Two identical sleds slide down two frictionless hills, each starting from rest at the top of its own hill. The first sled slides down a hill that is taller but has a gradual slope. The second sled slides down a hill that is shorter but has a steeper slope. Which sled reaches the bottom of its hill with the greatest speed? A)The second sled (shorter hill but steeper slope). B) It depends on the actual steepness of the hills, which is not given. C) The first sled (taller hill but gradual slope). D) Their final speeds will be the same.

Answer 1

Answer:

C) The first sled (taller hill but gradual slope).

Explanation:

As we know by Mechanical energy conservation law

initial total potential energy = final kinetic energy

so we know that

$mgH = \frac{1}{2}mv^2$

so we will have

$v = \sqrt{2gH}$

so from above equation we know that the the final speed is directly depending on the height of the object and it is independent of the slope of the plane

so here correct answer will be

C) The first sled (taller hill but gradual slope).