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netineya [11]
3 years ago
10

Marjorie drops an object from a height of h meters, and it hits the ground with a velocity of v m/s, as given by the function v

equals square root of 19.6 h. If the velocity of the object is 81.4 m/s, what was the height of the object before it was dropped? Round your answer to the nearest tenth.
Mathematics
1 answer:
Savatey [412]3 years ago
7 0

Answer:

The object was dropped at a height of 338.1 meters.

Step-by-step explanation:

According to the statement, the function velocity (v), in meters per second, in term of the initial height of the object (h), in meters, is represented by:

v = \sqrt{19.6\cdot h} (1)

This formula represents a particular case of a free fall analyzed by means of the Principle of Energy Conservation. If we know that v = 81.4\,\frac{m}{s}, then the height of the object before being dropped is:

h = \frac{v^{2}}{19.6}

h = 338.059\,m

The object was dropped at a height of 338.1 meters.

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