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Grade 12Differential Calculus

see attachment and explain with solution

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Profile image of Shivam
12 Years agoGrade 12
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1 Answer

Profile image of Jitender Singh
ApprovedApproved Tutor Answer12 Years ago
Ans: 6 km/hr
Let ‘x’ be the distance of the man from the lamp post at any moment & ‘l’ be the length of the shadow formed.
Distance of man from lamp post = x km
Distance of shadow from lamp post = (x+l) km
Height of the man = 1.5 km
Height of lamp post = 4.5 km
Using similar triangles, we have
\frac{x+ l}{l} = \frac{4.5}{1.5}
\frac{x+ l}{l} = 3
x = 2l
Differentiate on both sides, we have
\frac{dl}{dt} = \frac{1}{2}.\frac{dx}{dt}
\frac{dl}{dt} = \frac{1}{2}.4 = 2 (\frac{km}{hr})
Velocity of shadow:
\frac{d(x+l)}{dt} = \frac{dx}{dt} + \frac{dl}{dt} = 4 + 2 = 6(\frac{km}{hr})
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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