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On a frictionless horizontal surface , ...

On a frictionless horizontal surface , assumed to be the ` x-y` plane , a small trolley `A` is moving along a straight line parallel to the `y`-axis( see figure) with a constant velocity of `(sqrt(3)-1) m//s ` . At a particular instant , when the line `OA` makes an angle of `45(@)` with the `x` - axis , a ball is thrown along the surface from the origin `O`. Its velocity makes an angle `phi` with the `x` -axis and it hits the trolley .
(a) The motion of the ball is observed from the frame of the trolley . Calculate the angle `theta` made by the velocity vector of the ball with the `x`-axis in this frame .
(b) Find the speed of the ball with respect to the surface , if ` phi = (4 theta )//(3)`.

Text Solution

Verified by Experts

The correct Answer is:
(i) `45^(@)` (ii) `2 ms^(-1)`
(a) From the diagram `vec(V)_(BT)` makes an angle of `45^(@)` with the x-axis
(b) Using sine rule
`V_(B)/(sin 135^(@))=V_(T)/(sin 15^(@))`
`rArr V_(B)=2 m//s`
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