ok, draw the figure.
label the point of her shadow as x, and her position as y. Now make a triangle from the pole to the shadow. Notice the triangle formed by the girl and the shadow tip is SIMILAR to the large triangle.
So similar sides..
26:x::5:(x-y) (x is the full length, which includes y)
x/26=(x-y)/5
take the derivative with respect to time of the xpression..
dx/dt /26=(dx/dt-dy/dt)/5
check this, I am doing the algebra in my head..
dx/dt (1-26/5)= -26/5 dy/dt
you are given dy/dt as 7ft/sec
solve for dx/dt
A street light is at the top of a 26 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 7 ft/sec. At what rate is the tip of her shadow moving away from the light (ie. away from the top of the pole) when the girl is 23 ft away from the pole?
I know how to figure out the rate at which the shadow is lengthening from the base, which was the first part of this question, yet have no idea how to do the above part. Please help :( just a start would even be helpful i have no idea how to come at the problem.
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