Question

A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at

5 m2/s, how fast are the people moving when they are 5 m from the right angle? (Round approximations to two decimal places.)

Answer 1

1 m/s

Explanation:

the area of the triangle = A = ¹/₂ab

where a is the distance covered by the first person and b is the distance covered by the second person. since they walk at the same speed, then a = b, so our formula can be changed to A = ¹/₂x²

now we find the derivative of both sides:

dA/dt = ¹/₂ ⋅ dx²/dt

dA/dt = ¹/₂ ⋅ 2x ⋅ dx/dt

dA/dt = x ⋅ dx/dt = x ⋅ velocity

we are told that x = 5 m, and dA/dt = 5 m²/s

velocity = dA/dt / x

velocity = 5 m²/s / 5 m = 1 m/s