Imagine a tunnel that connects two points on the surface of the earth and passes through the centre of the earth. neglecting air resistance, the only force acting on a body of mass m in the tunnel is the gravitational force: f = -mgr/r. here g 9.8 ms? is the gravitational acceleration at the surface, r is the distance from the earth's centre, and r 6400 km is the radius of the earth. the position r(t) of a body in the tunnel is described by ř+ r=0. determine the general solution of this equation and solve the initial value problem r(0) = r, r(0) = 0. for these initial conditions, calculate the travel time between the two ends of the tunnel and the maximum speed reached in the course of the travel.