Tunnel through the Earth

What if we make a tunnel through the earth and drop a ball or any other body into it? How would the gravity behave on the ball, and , will the ball pop-up on the other side? If yes, then how much time will it take? A question, which is usually asked in competitive exams and for general interest.  This…

Fox – Rabbit Chase Problems

Part I: A fox chases a rabbit. Both run at the same speed $ v$ . At all times, the fox runs directly toward the instantaneous position of the rabbit , and the rabbit runs at an angle $ \alpha $ relative to the direction directly away from the fox. The initial separation between the fox and the rabbit is…