Suppose a police officer is 1/2 mile south of an intersection, driving north towards the intersection at 30 mph. at the same time, another car is 1/2 mile east of the intersection, driving east (away from the intersection) at an unknown speed. the officer's radar gun indicates 15 mph when pointed at the other car (that is, the straight-line distance between the officer and the other car is increasing at a rate of 15 mph). what is the speed of the other car?

In triangle ABC , using Pythagorean theorem

BC = sqrt(AB² + AC²)

r = sqrt(y² + x²)                                eq-1

taking derivative both side relative to "t"

dr/dt = (1/(2 sqrt(y² + x²) ) ) (2 y (dy/dt) + 2 x (dx/dt))

dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) (2 (0.5) (dy/dt) + 2 (0.5) (dx/dt))

dr/dt = (1/(2 sqrt(0.5² + 0.5²) ) ) ( v₁ + v₂)

15= (1/(2 sqrt(0.5² + 0.5²) ) ) ( - 30 + v₂)

v₂ = 51.2 m/s

1. Chemical energy from food is converted to mechanical energy when the food is broken down and absorbed in the muscles. 
2.The chemical energy from food can also be converted to thermal energy to keep the body warm.
3.When lightning strikes a tree, electrical energy is converted to thermal energy. 
4.Chemical energy stored within batteries can be converted to electrical energy. 
5.Electrical energy can be converted to light energy when a light is switched out.
6.Electrical energy can also be converted to sound energy when it is used to power a loudspeaker.
7.Sound energy is converted to electric energy in a microphone.
8.At hydroelectric water plants, gravitational potential energy is converted to electrical energy when water falls from a height.
9.Wind turbines convert the mechanical energy from the wind into electrical energy.
10.Solar panels convert light energy into electrical energy.
11.Electrical energy can be converted to mechanical and sound energy in a blender.
12.Chemical energy is converted to mechanical energy in cars when gasoline undergoes combustion to power the engine.
13.When fuels such as gasoline are combusted, chemical energy is converted to heat and light energy.
14.Nuclear energy is converted to heat and light energy in a nuclear reaction as seen in the sun and in atomic bombs.
15.Plants convert light energy to chemical energy through photosynthesis. 16.During bungee jumps, gravitational potential energy is converted to elastic potential energy.
17.Friction converts kinetic energy to thermal energy.
18.Waves convert mechanical energy to electrical energy.
19.Geothermal energy in geologically active regions of the world can be harnessed as electrical energy.
20.A ball dropped from a height is an example of a change of energy from potential to kinetic energy.