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A car C of mass m is initially at rest on the boat A of mass M tied to the identical boat B of some, mass M through a massless inextensible string as shown in the figure. The car accelerates from rest to velocity v_(0) with respect to boat A in time t_(0)sec. At time t=t_(0) the car applies brake and comes to rest relative to boat in negligible time. Neglect friction between boat and water find the velocity of boat A just after applying brake. |
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Answer» Solution :`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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