PLEASE EXPLAIN THE STEPS AND WRITE IT OUT [[[[LEGIBLY]]]]] !!!! Dr. Jones (mass

Question

PLEASE EXPLAIN THE STEPS AND WRITE IT OUT [[[[LEGIBLY]]]]] !!!!

Dr. Jones (mass mj) is trying to escape with his newly "borrowed" golden idol; he's running for his life as the locals are chasing him. Of course he thought ahead and has his hot air balloon (mass Mb, Mb mJ) all ready to go. He jumps in the wicker basket, fires the propane burners, and begins to ascend. Unfortunately, he forgot about the rope hanging down below the basket. Just as he thinks lie's safe, the biggest and meanest of the locals (mass m) grabs the rope and begins to climb toward the basket. As the balloon continues to ascend, Indy gets out his whip and repeatly attempts to strike his pursuer below him, who hangs just beyond reach. A minute later, about the time the balloon has reached its constant cruising altitude, Indy accidently drops his whip - losing it to the jungle far below. Consequently, the angry local begins to climb the rope with constant speed v relative to the rope. Show that the balloon takes on a downward component to its speed relative to the ground, given by vb=mv/m+mb.

Explanation / Answer

No net external force is acting on the combined system of balloon and angry local, since the downward acting gravitational force is counterbalanced by the air resistance acting upwards. So, we can apply principle of linear momentum. m*v = (m+Mb)*Vb => Vb = m*v/(m+Mb)

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