Person Walking From Wall Height Light Rate Of Change

How fast does the height of the person s shadow on the wall change when the person is 10 ft from the wall.

Person walking from wall height light rate of change.

You might call it the shadow problem or you might know it as the lamp post problem or maybe just the light problem guy or girl of a certain height walks. A 2 meter tall person is initially 10 meters from the wall and is moving towards the wall at a rate of 0 5 m sec. A light is mounted on a wall 5 meters above the ground. A spotlight is located on the ground 40 ft from the wall.

A spotlight is located on the ground 40 ft from the wall. After 4 seconds of moving is the tip of the shadow moving a towards or away from the person and b towards or away from the wall. Is the shadow increasing or decreasing in height at this time. The classic related rates problem.

If the person walks away from the the light as in our example his position x value is increasing and so dx dt is 1 5 m s a positive value. Example 7 a spot light is on the ground 20 ft away from a wall and a 6 ft tall person is walking towards the wall at a rate of 2 5 ft sec. The slider moves the person between the spotlight and the wall. A 5 ft tall person walks toward a wall at a rate of 2 ft sec.

James che brian alford and mani ramachandran torrey pines high school march 2011. The shadow height and its rate of change vary depending on the person s position. The only thing that changes is the sign of the rates. How fast does the height of the person s shadow on the wall change when the person is 10 ft from the wall.