47.1 Microsoft Word - MTH 251_lab_manual_cover.doc Activity 47 Solve each of the

Question

47.1

Microsoft Word - MTH 251_lab_manual_cover.doc Activity 47 Solve each of the following problems using procedures similar to those suggested in the previous problems Problem 47.1 It was a dark night and 5.5 ft tall Bahram was walking towards a street lamp whose light was perched 40 ft into the air. As he walked, the light caused a shadow to fall behind Bahram. When Bahram was 80 feet from the base of the lamp he was walking at a pace of 2 ft/s. At what rate was the length of Bahram's shadow changing at that instant? Make sure that each stated and calculated rate value has the correct sign. Make sure that your conclusion sentence clearly communicates whether the length of the shadow was increasing or decreasing at the indicated time. Problem 47.2 The gravitational force, F, between two objects in space with masses m and m2 is given by the formula F where r is the distance between the objects centers of mass and G is th

Explanation / Answer

let the distance of the man from the lamp-post be x
let the length of his shadow be y
by ratios:
5.5/y = 40/(x+y)
5.5x + 5.5y = 40y
5.5x = 34.5y
solving
55x = 345y
11x = 69y
11 dx/dt = 69 dy/dt

we have dx/dt =2ft/s
11(2) = 69 dy/dt
dy/dt = 22/69 ft/s --> rate at which the shadow is lengthening.

How fast is the shadow moving??
d(x+y)/dt = dx/dt + dy/dt
= 2+ 22/69 = 160/69 ft/s

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