Posted by **Equihua** on Friday, January 4, 2013 at 2:21pm.

A piece of elastic is attached to two nails on a flat board, with a button attached to the midpoint of the elastic. The ails are 5 cm apart. You stretch the elastic by pulling the button along the board i the direction that is perpendicular to the line between the nails.

A. Find the equation that relates the total length of the elastic x to the distance y that the button has moved.

B. You pull down the button at a constant 3cm/sec. Find the rate at which the length of the elastic is increasing when it is 12cm long.

- calculus -
**Steve**, Friday, January 4, 2013 at 2:36pm
each side of the elastic is the hypotenuse of a triangle with legs 5/2 and y, so

x = 2√(2.5^2 + y^2)

dx/dt = 2y/√(2.5^2+y^2) dy/dt

when x=12, y=5.45, so

dx/dt = 2(5.45)/6 (-3) = -1/5.45 = -0.18 cm/s

- calculus -
**:)**, Monday, August 10, 2015 at 7:18pm
A.

x = 2√[ y^2 + (2.5)^2 ] cm (using Pythagorus theorem)

B.

x^2 = 4y^2 + 25

=> 2x dx/dt = 8y dy/dt

=> dx/dt = 4 (y/x) dy/dt

When x = 12 cm, y = (1/2)√[ 144 - 25 ] = 2.727 cm

=> dx/dt = 4 (2.727/12) x 3 cm/s

= 2.727 cm/s.

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