Question

Two marbles are released from the same height. The first marble is released at time t = 0; the second marble is released at a later timet- (a) At timet i, what is the difference in the speeds of the two marbles? (you may use g to represent the magnitude of the acceleration of gravity.) (b) For times t is the difference in speeds larger, smaller or the same as the difference in the speeds in part (a)? (c) At timeにti, what is the separation in distance of the of the two marbles (the magni- tude of the difference between the displacements of the two marbles)? (d) For times t > ti is the separation in distance larger, smaller or the same as the separation in distance in part (c)? (e) Eventually the marbles hit the ground. Is the separation in time between when the first marble hits the ground and thesecond marble hits the ground larger than, smaller than or that same as At-ti?

Answer 1

at t = t_1 second marble just going to start so its speed will be = V_2 = 0 and speed of first marble t = t_1 will be v = 0 + gt_1 rightarrow gt_1 = v_1 so v_1 - v_2 = gt_1 - 0 = gt_1 b for time t > t_1 difference in speeds remains same as time passes because of acceleration due gravity acts on both c at t = t_1 displacement of second marble s_2 = 0 s_1 = 0 + 1/2 gt^2_1 = s_1 = gt^2_1/2 rightarrow s_1 - s_2 = gt^2_1/2 d t > t_1 separation is going to be because Delta s propto t^2 e both the marble take same time to travel same distance so Delta t = t_1