A person whose height is 6feet is walking away from the base of a street light along a straight path at a rate of 4 feet per second. If the height of a street light is 15feet, what is the rate at which a person’s shadow is lengthening?

xhl62d5k

xhl62d5k

Answered question

2023-02-12

A person whose height is 6feet is walking away from the base of a street light along a straight path at a rate of 4 feet per second. If the height of a street light is 15feet, what is the rate at which a person’s shadow is lengthening?

Answer & Explanation

Lavaroniuve

Lavaroniuve

Beginner2023-02-13Added 6 answers

Find the rate of change in length of shadow:
Let the distance from the pole be x and the length of the shadow be y
Using similar triangle property
Given : Height of a person =6feet
Walking at speed of 4feet/sec
dxdt=4feet/sec
Height of a streetlight =15feet
y6=x+y159y=6xy=2x3...(i)
Differentiate equation (i) with respect to time t, we get
dydt=23dxdt...(ii)
dydt=23×4[dxdt=4]
=83feet/sec
Hence, the rate at which a person's shadow is lengthening is 83feet/sec.

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