A piece of Lind is shaped like a right triangle. Two people start at the right a

Question

A piece of Lind 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 5 m^2/s, then how fast are the people moving when they are 3 m from the right angle? () 1.80 m/s 333 m/s 0.83 m/s 1.67 m/s Solve the problem. Round your answer, if appropriate. Water is discharged from a pipeline at a velocity v (in ft/sec) given by v = 1240p(1/2), where p is the pressure (in psi). If the water pressure is changing at a rate of 0.406 psi/sec, find the acceleration (dv/dt) of the water when p = 33.0 psi. 1450 ft/sec^2 35.6 ft/sec^2 108 ft/sec^2 43.8 ft/sec^2

Explanation / Answer

Let at some instant of time t, the persons be at a distance D from the right angle (Since they are both walking at the same speed, they will be equally far from the right angle)

Area of the triangle = (1/2)(D * D) = (1/2)(D^2)

Upon differentiation, (1/2)(2D) (dD/dt) = 5

D (dD/dt) = 5

But D = 3, so dD/dt = 5/3 = 1.67 m/s

Option (D).

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