Aman is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. as he approaches the parking lot of a market, he notices that the angle of depressions from his balloon to a friend's car in the parking lot is 35 ∘ . a minute and a half later, after flying directly over this friend's car, he looks back to see if friend getting into the car and observes the angle of depression to be 36 ∘ . at that time, what is the distance between him and his friend? (round to the nearest foot.)

Explanation:

Let at any moment of time the friend's car is at some horizontal distance "x" from the position of balloon.

Now if the altitude of the balloon is fixed and it is at height "h"

so here we will have

now we know that

initially the angle of the friend's car is 35 degree

so the horizontal distance will be

similarly if the angle after passing the car position is 36 degree

then we have

now the speed of the balloon is constant

so we have

so the final position of friend when the angle is 36 degree

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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