Question

How to do 180th question?

Answer 1

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!!