(Solved): A woman stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of ...

A woman stands at the edge of a cliff and throws a rock horizontally over the edge with a speed of \( v_{0}=15.5 \mathrm{~m} / \mathrm{s} \). The rock leaves her hand at a height of \( h=53.0 \mathrm{~m} \) above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the rock leaves the hand. (a) What are the coordinates of the initial position of the rock? (Enter your answers in \( \mathrm{m} \).) \[ \begin{array}{ll} x_{0}= & m \\ y_{0}= & m \end{array} \] (b) What are the components of the initial velocity? (Enter your answers in \( \mathrm{m} / \mathrm{s} \).) \[ \begin{array}{ll} v_{0 x}= & \mathrm{m} / \mathrm{s} \\ v_{0 y}= & \mathrm{m} / \mathrm{s} \end{array} \] (c) Write the equations for the \( x \) - and \( y \)-components of the velocity of the rock with time. (Use the following as necessary: \( t \). Assume that \( v_{x} \) and \( v_{y} \) are in \( \mathrm{m} / \mathrm{s} \) and \( t \) is in seconds. Do not include units in your answers.) \[ v_{x}= \] \( \mathrm{m} / \mathrm{s} \) \[ v_{y}= \] (d) Write the equations for the position of the rock with time, using the coordinates in the figure. (Use the following as necessary: \( t \). Assume that \( x \) and \( y \) are in meters and \( t \) is in seconds. Do not include units in your answers.) \[ \begin{array}{l} x= \\ y= \end{array} \] What is the acceleration? What is its direction? What equation relates the \( y \)-displacement to the acceleration in the \( y \)-direction, the initial velocity in the \( y \)-direction, and the time? \( \mathrm{m} \) (d) Write the equations for the position of the rock with time, using the coordinates in the figure. (Us e following necessary: \( t \). Assume that \( x \) and \( y \) are in meters and \( t \) is in seconds. Do not include units in your wers.) \[ \begin{array}{l} x= \\ y= \end{array} \] What is the acceleration? What is its direction? What equation relates the y-displacement to the accelerati \( y \)-direction, the initial velocity in the \( y \)-direction, and the time? \( \mathrm{m} \) e) How long (in s) after being released does the rock strike the ground below the cliff?