0O AT&T; LTE 3796 E 6:05 PM ww3.math.msu.edu > webwork /mth_132 ss16 64040/ hw14
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0O AT&T; LTE 3796 E 6:05 PM ww3.math.msu.edu > webwork /mth_132 ss16 64040/ hw14 2.8 related_rates /8 Hw14 2.8 Related rates: Problem 8 Previous Problem List Next uS Problem List Next (1 point) Get help entering answers See a similar example (.PDF) A street light is at the top of a pole that is 11 feet tall. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the length of her shadow moving when she is 35 ft from the base of the pole? ANSWER: ft/sec. Preview My Answers Submit Answers Show me another You have attempted this problem 0 times. You have 20 attempts remaining.Explanation / Answer
Put a 11 ft high pole on the left with the light on. Draw a pathway to the right. At any given time, the 6 ft high woman is L feet from the light. She casts a shadow of length sl. With respect to the light, a right triangle is formed which has one side of 11 ft, a second side (on the ground) of L+sl.
We want to find how fast L+sl changes at a L=35 ft, if L is increasing at 6 ft/sec.
From the picture, it should be evident that, by similar triangles, (L+sl)/11 = sl/6. After separating variables, you can show that L =(5/6) sl. So then
dL/dt = (5/6) d(sl)/dt.
For the conditions at hand, when L=35 ft, L+sl= 64.16 feet, If dL/dt=6, dsl/dt=7.2..Therefore, the tip will be moving at 13.2 ft/sec.
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