The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.
(b) When <em>x </em>= 0.6 and q = 0.5 m/s, the speed of the wagon is approximately <u>0.243 m/s</u>.
Reasons:
(a) The distance from the cart to the pulley, <em>r</em> is given by Pythagoras's
theorem as follows;
r = √((3 - 0.6)² + x²) = √(2.4² + x²)
The speed of the wagon =
The speed of the rope, q =
By chain rule, we have;
Therefore;
(b) The speed of the wagon when <em>x</em> = 0.6 if q = 0.5 m/s is given as follows;
The speed of the wagon when <em>x </em>= 0.6 and q = 0.5 m/s, ≈ <u>0.243 m/s</u>
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