2. 10 points] (Related Rates) A man of height 1.9 m walks away from a 5 m lamppo

Question

2. 10 points] (Related Rates) A man of height 1.9 m walks away from a 5 m lamppost at a speed of 1.3 m/s. Find the rate at which his shadoow is increasing in length. Let a denote the distance from the lamppost to the man and y denote the distance from the man to the tip of his shadow. (a) What is the given rate and what is the rate we want to kmow (in ternms of differentials)? (b) Use sinilar triangles to find an equation relating r and y (c) Implicitly differentiate the equation from part (b) to get an equation relating the differ- entials from part (a). (d) Solve, rounding your final answer to 3 decimal places. Write a sentence explaining your answer.

Explanation / Answer

a. dx/dt =1.3m/s , dy/dt is unknown

b. 5/1.9 = (x+y/x)= 1+(y/x)

c. (5/1.9)-1 = y/x

3.1/1.9 = y/x

y= (3.1/1.9) x

dy/dt =(3.1/1.9)(dx/dt)

dy/dt = (3.1/1.9)(1.3)

dy/dt = 2.121m/s

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