question_answer 49)

                  A ball is dropped from a building of height 45 m. Simultaneously anther ball is thrown up with a speed 40 m/s. Calculate the relative speed of the balls as a function of time.                    

Answer:

                  For a ball dropped from a building, speed in the downward direction after time t is given by                 \[{{\upsilon }_{{{y}_{1}}}}=\,0\,+\,gt\,=\,\,-\,10t\]                 For a ball thrown up with \[\upsilon =40\,m{{s}^{-1}}\],                 Speed after time t is given by \[{{\upsilon }_{{{y}_{2}}\,}}=\,40\,-\,10t\]                 \ Relative speed of balls \[={{\upsilon }_{{{y}_{2}}}}-{{\upsilon }_{{{y}_{1}}}}\]\[=40\,m{{s}^{-1}}\]