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On a frictionless horizontal surface, as...

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 `(sqrt3 - 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 trolley. Calculate the angle 0 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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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 )//(4) .

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