Math  /  Geometry

Question2. A bright light sits on the ground ten metrgs from a tall, vertical post. A child of height 1.6 metres walks from the post directly toward the light, casting a shadow on the pole. How far is the child from the light when the height of the shadow is increasing at the same rate as the child is walking forward?

Studdy Solution
Re-evaluate the setup: Correct the differentiation and solve again. Assume positive values for distances and rates.
Re-solve the equation:
1.6x2=110\frac{1.6}{x^2} = \frac{1}{10}
Multiply both sides by x2 x^2 :
1.6=x2101.6 = \frac{x^2}{10}
Multiply both sides by 10:
16=x216 = x^2
Take the square root:
x=16=4x = \sqrt{16} = 4
The child is 4 meters from the light when the height of the shadow is increasing at the same rate as the child is walking forward.

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