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related rates: A spotlight on the ground shines on a wall
- Thread starter sickplaya
- Start date
Related rates...
Let x(t) be the distance from the spotlight to the man at time t. Suppose t=0 when he's right near the light. Let h(t) denote the height of his shadow.
We know dx/dt = 1.6, we want dh/dt when x=4.
Draw a picture and use similar triangles to see that x/12 = 2/h at any t.
Then h(t) = 24/x(t). Differentiate, using chain rule.
Let x(t) be the distance from the spotlight to the man at time t. Suppose t=0 when he's right near the light. Let h(t) denote the height of his shadow.
We know dx/dt = 1.6, we want dh/dt when x=4.
Draw a picture and use similar triangles to see that x/12 = 2/h at any t.
Then h(t) = 24/x(t). Differentiate, using chain rule.
sickplaya said:i got an answer of -0.6m/s; is it correct or not
Not.
You get -2.4 m/s.
sickplaya said:... but the question is 4m from the building
My bad! You're right, -0.6 m/s in that case because you need dh/dt when x=12-4=8.