Question

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.

Answer 1

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.