Question

if a boy rides a sled down a steep hill, then which of the following takes place during the childs ride?

a potential energy decreases and kinetic energy increases.

b potential energy increases and kinetic energy decreases.

c both kinetic and potential energy increase.

d both kinetic and potential energy decrease.

Explanation:

To solve this, we recall the concepts of potential and kinetic energy. Potential energy (PE) depends on height ($PE = mgh$, where $m$ is mass, $g$ is gravity, $h$ is height) and kinetic energy (KE) depends on velocity ($KE=\frac{1}{2}mv^{2}$, where $v$ is velocity). When the boy rides down the hill:

• His height ($h$) decreases, so potential energy (which is proportional to height) decreases.
• His speed ($v$) increases (since he is moving down the steep hill), so kinetic energy (proportional to the square of velocity) increases.

Now let's analyze each option:

• Option a: Says potential energy decreases and kinetic energy increases. This matches our analysis.
• Option b: Claims potential energy increases (but height is decreasing) and kinetic energy decreases (but speed is increasing). Incorrect.
• Option c: Says both increase. But height is decreasing (so PE should decrease) and speed is increasing (KE increases), so both can't increase. Incorrect.
• Option d: Says both decrease. But speed is increasing (so KE should increase), so this is incorrect.

Answer:

a. Potential energy decreases and kinetic energy increases.