Suppose it is possible to dig a smooth tunnel through the earth from a city at A to a ci...

Suppose it is possible to dig a smooth tunnel through the earth from a city at A to a city at B as shown. By the theory of gravitation, any vehicle C of mass m placed within the tunnel would be subjected to a gravitational force which is always directed toward the center of the earth D. This force F has a magnitude that is directly proportional to its distance r from the earth's center. Hence, if the vehicle has a weight of W = mg when it is located on the earth's surface, then at an arbitrary location r the magnitude of force F is F = (mg / R)r , where R = 6328 km, the radius of the earth. If the vehicle is released from rest when it is at B, x = s = 2 Mm, determine the time needed for it to reach A, and the maximum velocity it attains. Neglect the effect of the earth's rotation in the calculation and assume the earth has a constant density. Hint: Write the equation of motion in the x direction, noting that r cos θ = x Integrate, using the kinematic relation v dv = a dx, then integrate the result using v = dx/dt.