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A ball is thrown upwards with a speed of...

A ball is thrown upwards with a speed of `40m//s`. When the speed becomes half of the initial speed, gravity is switched off for next 2 second. After that gravity is again switched on but magnitude gravity is doubled. The total distance travelled by the ball from `t=0` to the time when the ball reaches the maximum heighth is `55beta`. Find the value of `beta`.

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