Question
- A spot Light is on the ground
away from a wall and 6 FT )
person is walking towards the wall at a rate of
. How fast is
the height of the shadow changing when the person is 8 fT from the wall?
Is the shadow increasing or decreasing in height at this Time?
person is walking towards the wall at a rate of
the height of the shadow changing when the person is 8 fT from the wall?
Is the shadow increasing or decreasing in height at this Time?
Ask by Harrington Mills. in the United States
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When the person is 8 ft from the wall, the height of the shadow is decreasing at a rate of 0.75 ft/sec.
Solution

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Bonus Knowledge
To solve this problem, we can use similar triangles. Let
be the height of the shadow and
be the distance of the person from the wall. The light, the top of the person’s head, and the tip of the shadow all form similar triangles.
Using the distances, we can set up the relation:
As the person walks towards the wall,
decreases. The rate of change of
is given as
.
To find the rate of change of the shadow’s height, we differentiate
with respect to time
:
Substituting
:
So, the height of the shadow is decreasing at a rate of
when the person is 8 ft from the wall.