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A car of mass m is initially at rest on ...

A car of mass `m` is initially at rest on the boat of mass `M` tied to the wall of dock through a massless, inextensible string. The car accelerates from rest to velocity `v_(0)` in times to. At `t = t_(0)` the car applies brake and comes to rest relative to the boat in negligible time. Neglect friction between the boat and water: the time `'t'` at which boat will strike the wall is

Text Solution

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`A` the car `C` accelerates to a velocity `v_(0)` relative to the double-boat system, the two boats accelerate to the left.
`V_(C )("to right")+v_(A)("to left")=v_(0)`
`Mv_(C )=2Mv_(A)`
Solving, we find `v_(A)=(mv_(0))/(m+2M)`, `v_(C )=(2Mv_(0))/(m+2M)`
After the car brakes to a stop, the tension in the string connecting `A`, `B` becomes zero. Applying We find the velocity of `A`(to right) :
`v'_(A)=(mMv_(0))/((m+M)(2+2M))`
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