Answer:
The shadow is increasing with the rate of 4 m/min
Step-by-step explanation:
Consider x represents the length of the boy from the lamp and y represents the length of his shadow,
Given,
The height of boy = 1 m,
The height of lamp = 6 m,
By making the diagram of this situation,
We get two similar triangles one having sides 6 and x+y , and other having sides 1 and y,
Since in similar triangles corresponding sides are in same proportion,
Thus,
[tex]\frac{6}{x+y}=\frac{1}{y}[/tex]
[tex]6y=x+y[/tex]
[tex]6y-y=x[/tex]
[tex]5y=x[/tex]
[tex]\implies y=\frac{x}{5}[/tex]
Differentiate with respect to t (time),
[tex]\frac{dy}{dt}=\frac{1}{5}\frac{dx}{dt}[/tex]
We have [tex]\frac{dx}{dt}=20\text{ m per min}[/tex]
[tex]\frac{dy}{dt}=\frac{1}{5}(20)=4\text{ m per min}[/tex]
