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Solution :

With the given details, we can draw a right angle triangle.<br>
Please refer to video to see the traingle.<br>
From the diagram,<br>
`x^2+y^2 = 6^2`<br>
Here, `x = 4`<br>
`:. y = sqrt(6^2-4^2) = sqrt20 = 2sqrt5 m`<br>
Now, we can create an equation using pythagoras theorem.<br>
`x^2+y^2 = 6^2->(1)`<br>
Now, differentiating (1),<br>
`=>2xdx/dt +2ydy/dt = 0`<br>
It is given that `dx/dt = 0.5` m/sec , `x = 4 m and y = 2 sqrt5 m`.<br>
`:. 2(4)(0.5) + 2(2sqrt5)dy/dt = 0`<br>
`=>dy/dt = -(4sqrt5)/4= -1/sqrt5` m/sec.<br>
So, the rate at which the top sliding downwards is `-1/sqrt5` m/sec.<br>**Introduction: average rate and instantaneous rate**

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