An object of mass m 2 kilograms moves vertically (with respect to the ground) under the action of the earth gravitational acceleration of magnitude g = 10 meters per second squared. Denote by y vertical coordinate, positive upwards, and let y = 0 be at the earth surface. Recall that the force on the object in this situation is f-mg, where the negative sign says the force points downwards. (a) Write the differential equation satisfied by this system. 10 Note: Write t for t, write y for y(), and yp for y'(t) (b) Find the mechanical energy E of this system. E(t) 112)(2)(yp)^2+(2)(10)(y) Note: Write t for t, write y for y(t), and yp for y) (c) If the initial position of the object is y 0) = 0 meters and its initial velocity is y, 0) 5 meters per second, find the maximum altitude ymax > 0 achieved by the object. ymax-1/2