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23.07.2019 •
Mathematics
Aperson whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. if the height of a streetlight is 15 feet, what is the rate at which a person’s shadow is lengthening?
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Ответ:
s/6=(x+s)/15
thus
5s=2x+2s
3s=2x
hence
ds/dt=2/3 dx/dt
but
dx/dt=4 ft per second
hence
ds/dt=2/3*4=8/3
Ответ:
The rate at which a person’s shadow is lengthening is
Step-by-step explanation:
Given :
Height of a person = 6 feet
Walking at speed of 4 feet/sec.
Height of a streetlight = 15 feet
Calculation :
Let the distance from the pole be x and the length of the shadow be y.
Using similar triangle property
Differentiate equation (1) with respect to time, we get
Here,
From equartion (2), we get
The rate at which a person’s shadow is lengthening is
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