Related Rates Question:

A new year's observer watches a large light drop at a constant rate from the top of a tower of unknown height unto a platform 60 feet away, and 6 feet above the ground, which is also the height of the observer. The ball drops for 10 seconds (10-second countdown), and the observer sees that the shadow they cast in the light is growing at 4.5 feet per second after 5 seconds (half of the light's journey down the tower). What is the height of the tower, and the rate at which it descends?

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Related Rates Question:

A new year's observer watches a large light drop at a constant rate from the top of a tower of unknown height unto a platform 60 feet away, and 6 feet above the ground, which is also the height of the observer. The ball drops for 10 seconds (10-second countdown), and the observer sees that the shadow they cast in the light is growing at 4.5 feet per second after 5 seconds (half of the light's journey down the tower). What is the height of the tower, and the rate at which it descends?