$6.$ A small rock with mass $0\mathrm{.}12$ kg is fastened to a massless string with length $0\mathrm{.}80$ m to form a pendulum. The pendulum is swinging so as to make a maximum angle of $=45$ with the vertical. Air resistance is negligible. $($a$)$ What is the speed of the rock when the string passes through the vertical position? $($b$)$ What is the tension in the string when it makes an angle of $45$ with the vertical? $($c$)$ What is the tension in the string as it passes through the vertical?