Suppose it is possible to dig a smooth tunnel through the earth from a city at A to a city at B as shown.(Figure 1) 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. Part A) 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. 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 rcosθ=x. Integrate, using the kinematic relation vdv=adx, then integrate the result using v=dx/dt. Part B) Determine the maximum velocity the vehicle attains

Suppose it is possible to dig a smooth tunnel through the earth from a city at A to a city at B as shown.(Figure 1) 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. Part A) 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. 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 rcosθ=x. Integrate, using the kinematic relation vdv=adx, then integrate the result using v=dx/dt. Part B) Determine the maximum velocity the vehicle attains