Recall the dangerous ladder from homework #3. Its length is 2A and its mass is . To transport the ladder back to your truck, you rest one end of the ladder atop a barrel, lift the opposite end until the ladder is horizontal, and walk toward the barrel, pushing the ladder as shown: A friend is standing by to support the ladder on the other side of the barrel as you move forward. The ladder rolls atop the barrel without slipping and the barrel rolls along the ground without slipping. Let R denote the barrel's radius, M the barrel's mass, Iem the barrel's rotational inertia relative to its center, and F the magnitude of the force with which you're pushing the ladder. Find Lagrange's equation corresponding to the barrel's angle of rotation o, and thus obtain a formula for & in terms of F and the various constants defined above. You can assume that increases as the ladder advances. If the barrel is initially all the way at the forward end of the ladder, how far will the ladder advance before the back end falls off the barrel?