The answer is dy/dt is equal to -(20/7)(1/14)(0.6) = -0.12245 m/s.
The negative sign shows that the rate is falling as y gets shorter
.Woman Height/ Distance Light To Woman equals
Shadow Height/Distance Light To Wall.
explanation?
Think of a huge triangle with the origin as the spotlight, a base of 20, and the height of the shadow on the wall as y. Inside the larger triangle, a comparable triangle that is x meters from the spotlight and 2 meters
tall—the woman's height—can be seen.
Woman Height/ Distance Light To Woman equals
Shadow Height/Distance Light To Wall.
The shadow height is y. Let x be the distance from the woman to the light.
xy = 40 or y/20 = 2/x
Take both sides' derivative:
XDY + YDX = 0 based on the product rule.
Solve for the desired result, dy/dy:
dy/dt = -(y/x)dx/dt, where dx/dt = 0.6 m/s.
The woman is 20 - 6 meters from the light when she is 6 meters from the wall, which is 14 meters, or x.
Keep in mind that y/20 = 2/x = 2/14 --> y = 40/14 = 20/7 from the related triangles.
So, dy/dt is equal to -(20/7)(1/14)(0.6) = -0.12245 m/s.
The negative sign shows that the rate is falling as y gets shorter.
To learn more about find length of her shadow refer to:
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