Light Base
How do i solve:At what rate is the length of her shadow changing when she is 15 ft from the base of the light?
A woman 5.5 ft tall walks at a rate of ft/sec toward a streetlight that is 22 ft above the ground. At what rate is the length of her shadow changing when she is 15 ft from the base of the light? (round to the nearest .5 ft/sec if necessary)
the rate is 6ft/sec
You write an equation for the length of her shadow and take its time derivative.
Let x = distance from street light.
Let s = length of shadow. You can write an expression for s using trigonometry. s will be a function of x.
Then ds/dt = (ds/dx)(dx/dt)
You know dx/dt, that’s … well, you didn’t put the number, but it’s the speed she’s walking.
And ds/dx is the derivative of s(x).
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