# Lesson Worksheet: Conservation of Energy Mathematics

In this worksheet, we will practice applying the conversion of energy principle to solve problems on moving bodies.

**Q5: **

A body of a mass of 20 kg was projected vertically upward from the ground with a velocity of 30 m/s. It passed by a point A when its velocity was 10 m/s.

Calculate the potential energy of the body at point A. Neglect the air resistance and consider
the acceleration due to gravity to be 9.8 m/s^{2}.

Find the distance between point A and the ground surface, in meters, Give your answer to one decimal place.

**Q7: **

A car descended 195 m on a slope from rest, which is equivalent to a vertical distance of 14 m. Given that of the potential energy was lost due to resistance and that the resistance remained constant during the carβs motion, determine the carβs velocity after it had traveled the mentioned distance of 195 m. Take .

**Q9: **

A body started sliding down the line of greatest slope of a smooth inclined plane. When it was at the top of the plane, its gravitational potential energy relative to the bottom of the plane was 1,830.51 joules. When it reached the bottom of the plane, its speed was 8.6 m/s. Find the mass of the body.

**Q10: **

A body was projected up a rough inclined plane from its bottom. Its initial kinetic energy was 242 joules. The body continued moving until it reached its maximum height and then slid back down to the bottom. When it reached the bottom, its kinetic energy was 186 joules. Find the work done against friction during the ascent and the gain in gravitational potential energy when the body was at its maximum height.

- A,
- B,
- C,
- D,