question_answer

 A railway carriage moves over a straight, track with acceleration a. A passenger in the carriage drops a stone. What is the acceleration of the stone w. r. t. the carriage and the earth?

Answer:

                When the stone is dropped, it falls freely under the acceleration due to gravity g. With respect the earth, the acceleration of the stone is g. Inside the carriage, the stone possesses two accelerations: (i) Horizontal acceleration \['a'\] due to the motion of the carriage. (ii) Vertical downward acceleration 'g' due to gravity. The acceleration of the stone w. r. t. the carriage \[=\sqrt{{{a}^{2}}+{{g}^{2}}}\]