Respuesta :
The speed of man when the length of his shadow on the building decreases when he is 4 m from the building will be 0.6 m/sec.
What is velocity?
The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
Distance from spot shines = 12 m away
Height of man,h=2 m tall
Speed of man +1.6 m/s,
Distance from the building = 4 m
Let the height of shadow= y,
CD=x
Height of man=2 m
Speed of man:
[tex]\rm \frac{dx}{dt} = 1.6 \ m/sec[/tex]
As the triangle ABD and ECD are similar. The property of the similarity is found as;
[tex]\rm \frac{y}{2} = \frac{12}{x} \\\\ xy = 24[/tex]
Differentiate the above question with respect to x;
[tex]\rm x \frac{dy}{dt}+y\frac{dx}{dt}=0 \\\\ x\frac{dy}{dt}= -y\frac{dx}{dt}[/tex]
From the given conditions the man is 4 m from the building the value of the remaining distance x is;
x=12-4
x=8 m
Speed of man:
[tex]\rm \frac{dx}{dt} = 1.6 \ m/sec[/tex]
On putting all the values we get;
[tex]\rm \frac{y}{2} = \frac{12}{x} \\\\ xy = 24 \\\\ 8y = 24 \\\\ y= 3[/tex]
The speed of man when the length of his shadow on the building decreases when he is 4 m from the building;
[tex]\rm \frac{dy}{dt} = - \frac{3}{8} \times 1.6 \ m/sec \\\\\ \frac{dy}{dt} = 0.6 \ m/sec.[/tex]
Hence the value of the speed for the given conditions willl be 0.6 m/sec.
To learn more about the velocity, refer to the link: https://brainly.com/question/862972.
#SPJ1
