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A light is hung 15 ft above a straight horizontal path. If a man 6 ft tall is walking away from the light at the rate of 5 ft/s...Asked by tante
a light is hung 15 feet above a straight horizontal path. If a man is 6 feet tall is walking away from the light at a rate of 5 feet/sec.
a) how fast is his shadow lengthening?
b) at what rate is the tip of the man's shadow moving?
a) how fast is his shadow lengthening?
b) at what rate is the tip of the man's shadow moving?
Answers
Answered by
oobleck
Let
x = distance from light
s = length of shadow
Then
(x+s)/15 = s/6
s = 2/3 x
(a) ds/dt = 2/3 dx/dt = 2/3 * 5 = 10/3 ft/s
(b) 5 + 10/3 = 25/3 ft/s
x = distance from light
s = length of shadow
Then
(x+s)/15 = s/6
s = 2/3 x
(a) ds/dt = 2/3 dx/dt = 2/3 * 5 = 10/3 ft/s
(b) 5 + 10/3 = 25/3 ft/s
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