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Two balls are thrown simultaneously, A v...

Two balls are thrown simultaneously, A vetically upwards with a speed of `20 ms^(-1)` from the ground, and B vetically downwards from height of 40 m with the same speed and along the same line of motion. At what points do the two balls collide? Take `g= 9.8 ms^(-2)`.

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Suppose the two balls meet at a height of x from the ground after time t s from the start. For upward motion of balls A :
`u=20ms^(-1),g=9.8ms^(-2)`
`s=ut+1/2"gt"^2`
`x=20t-1/2xx9.8t^2=20t-4.9t^2`

For downward motion of ball B
`40-x=20xxt+1/2xx9.8t^2`
`=20t+4.9t^2`
Adding (i) and (ii) 40=40 or t=1s
From (i), x=`20xx1-49xx(1)^2=15.1m`
Hence the two balls will collide after 1 s at a height of 15.1 m from the ground.
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