question_answer 56)

                  A girl riding a bicycle along a straight road with a speed of \[5\text{ }m{{s}^{1}}\] throws a stone of mass 0.5 kg which has a speed of \[15\text{ }m{{s}^{1}}\] with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?

Answer:

                  Initial momentum of the system (bicycle + girl + stone)                 \[=50.5\times 5=252.5\text{ }kg\text{ }m{{s}^{-1}}\]                 Let \[\upsilon =\] speed of bicycle + girl after the throw.                 Final momentum of the system                 \[=(50\upsilon +0.5\times 15)\text{ }kg\text{ }m{{s}^{1}}\]                 \[=(50\upsilon +7.5)\text{ }kg\text{ }m{{s}^{1}}\]                 According to the law of conservation of momentum                 \[50\upsilon +7.5=252.5\] or \[\upsilon =\frac{245}{50}\,\,=\,4.9\,\,m{{s}^{-1}}\]                 Change in the speed of bicycle \[=54.9=0.1\,\,m{{s}^{1}}\]