The arrow is fired from the bow vertically upward at a speed of 30 m / s.

The arrow is fired from the bow vertically upward at a speed of 30 m / s. Determine to what height the arrow has risen and for what period of time?

Given:

v = 30 m / s (meters per second) – the speed of an arrow fired from a bow.

It is required to determine h (meter) – the maximum height to which the boom will rise, as well as t (seconds) – the lifting time.

Since the condition of the problem is not specified, we will not take into account the resistance forces during operation.

Then, according to the law of conservation of energy, the kinetic energy of the arrow at the surface of the earth will be equal to the potential energy at the maximum height:

Ekinetic = Epotential;

m * v ^ 2/2 = m * g * h, where m is the mass of the arrow, g = 9.8 Newton / kilogram;

v ^ 2/2 = g * h;

h = v ^ 2 / (2 * g);

h = 30 ^ 2 / (2 * 9.8) = 900 / 19.6 = 45.9 meters (the result has been rounded to one decimal place).

Then the ascent time will be equal to:

t = v / g = 30 / 9.8 = 3.1 seconds.

Answer: The boom will reach its maximum height of 45.9 meters in 3.1 seconds.