AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

A point source of light is hung 30 feet directly above a straight horizontal path on which a man of 6 feet in height is walking. How fast is the man’s shadow lengthening and how fast the tip of the shadow is moving when he is walking away from the light at the rate of 100ft/min. , .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let s be the point source of light
Rate of walking =100 ft/min
In △ASC & △BDC

\frac{AS}{BD}

\frac{AC}{BC}

\frac{30}{6}

\frac{y}{x + y}

⇒ 5y=x+y
⇒ 4y=x
4

\frac{dy}{dx}

\frac{dx}{dt}

=100 ⇒

\frac{dy}{dt}

=25 ft/min (Length of shadow moves at rate dy/dt)
Now Let AC=z
Now BC=AC−AB=z−x
Now Again IN △ASC & △BDC

\frac{AS}{BD}

\frac{AC}{BC}

\frac{30}{6}

\frac{z}{z - x}

⇒ 4z= 5x
Now

\frac{dz}{dt}

= 125 ft/min (Rate of change of shadow)
Hence, The correct answer is option (1).

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!