Question

A piece of land is shaped like a right triangle. Two people start at the right angle of the triangle at the same​ time, and walk at the same speed along different legs of the triangle. If the area formed by the positions of the two people and their starting point​ (the right​ angle) is changing at 2 m squared divided by a comma then how fast are the people moving when they are 3 m from the right​ angle

Answer 1

Answer:

They are moving at a speed of 2/3 meters per second.

Step-by-step explanation:

The field is shown in the attached figure below

As we can see that ant any instant of time Area of the triangle is given by

$A=\frac{1}{2}x\times x\\\\A=\frac{1}{2}x^2$

Differentiating both sides of the above equation with respect to time we get

$\frac{dA}{dt}=\frac{1}{2}\cdot \frac{dx^2}{dt}\\\\\frac{dA}{dt}=\frac{1}{2}\cdot 2x\cdot \frac{dx}{dt}\\\\\frac{dA}{dt}=x\cdot v$

Applying values in the given relation we get

$v=\frac{A'}{x}=\frac{2}{3}=\frac{2}{3}m/s$