Question #42428

A block of mass $M = 18.75 \text{ kg}$ rests on a smooth horizontal table. A long, light string of linear mass density $\mu = 0.01 \text{ kg/m}$ is attached to the block, passes around a light movable pulley, and has its other end fixed to a vertical wall. The string segments are horizontal. At $t=0$, the movable pulley is pulled away from the wall with a time-varying acceleration $a_p = 6t \text{ m/s}^2$. At the exact same instant $t=0$, a transverse wave pulse is generated at the block. The initial distance between the block and the pulley is $L_0 = 101 \text{ m}$. Assuming the tension is uniform along the string at any given instant, find the time $t_0$ when the pulse reaches the pulley.