4. A ball on Earth is thrown vertically upward from a height of 12 feet with an initial velocity of 30 feet per second. Assume the acceleration due to gravity = -32 feet per second per second. Neglect air resistance. a. Find the height function in terms of time. h" 4 (t ) = h'4 (t ) = h ' 4 ( 0 ) = 15 ; h 's ( t ) = 12 ha (t ) = h4 (0) = 6; h4(t) = b. What time does the ball reach maximum height? h'4(c) = 0; c=_ c. Find the maximum height of the ball. ha (c ) = d. How long will it take for the ball to hit the ground? ha(t) = 0, t = =btvb2-4ac 2a