A ball is thrown upward from a height of \( 640 \) feet above the ground, with an initial velocity of \( 96 \) feet per second. From physics it is known that the velocity at time t is \(v ( t ) = 96 - 32 t\) feet per second.
a) Find \( s ( t ) \) , the function giving the height of the ball at time t.
b) How long will the ball take to reach the ground?
c) How high will the ball go?