A block slips along an incline of a wedge. Due to the reaction of the block on the wedge, it slips backwards. An observer on the wedge will see the block moving straight down the incline. Discuss how to find the absolute velocity of the block.
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Explanation

We know that `vec v_(m//M) = vec v_m - vec v_M rArr vec v_m = vec v_(m//M) + vec v_M`
Note that a single subscript implies absolute velocity. The absolute velocity of block is the vector sum of its velocity relative to the wedge and velocity of wedge relative to ground.
The absolute velocity of block (ground reference frame) is shown in the vector diagram given in (Fig. 5.80).
`|vec v_m| = sqrt(v^2 + V^2 + 2 v V cos (pi - theta))`
=`sqrt(v^2 + V^2 - 2 v V cos theta)`
We can derive this result by resolving `v` into its components.
Sum of x - components `V_x = v cos theta - V`
Sum of y - components `V_y = v sin theta`
Resultant velocity `= sqrt(V_x^2 + V_y^2)`
=`sqrt((v cos theta - V)^2 + (v sin theta)^2))`
=`sqrt(v^2 + V^2 - 2 v V cos theta)`
`tan prop = (V_y)/(V_x) = (v sin theta)/(v cos theta - V)`.
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