How to do 180th question?

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1 Answer
Mar 28, 2018

Its an interesting question...ANS must be 15cm/s.

Explanation:

According to the question, R=10 (it doesn't matter for the slope), so the circle is given by #x^2 + y^2 = R^2 = 100#.

Since, height=#2cm#, we are looking for the slope of the tangent line through the point with y=-8, which is (-6,-8).

Now the slope is given by #-x/y = -6/8#.

Now, given a velocity of 20m/s to the left, we know that the sphere will have a velocity of #6/8 * 20m/s# = 15m/s.

  • YOU MAY BE THINKING WHY IS THE VELOCITY ??

#6/8 * 20m/s# = 15m/s.

  • WELL HERE'S WHY ,

Let's say the height of the intersection of the wedge and the circle at a given time is #H#, and the wedge moves over axis #X#.

We know the slope of the sphere is #6/8#, so #dh/dx=6/8#, #dh=6/8*dx#.
The velocity of the wedge is given by #dx/dt=20m/s#. The velocity of the sphere is given by dh/dt.

We know #dh/dt = 6/8*dx/dt = 6/8*20m/s = 15m/s#.

I HOPE IT HELPS!!