An arrow fired vertically upward from the bow fell to the ground after 6 seconds.

An arrow fired vertically upward from the bow fell to the ground after 6 seconds. Determine the maximum h lift of the boom and the distance traveled.

Given:

t = 6 seconds – flight time of an arrow released vertically upward;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the maximum lifting height of the boom H and and the distance traveled S (meters).

Since the flight time of the arrow is equal to the fall time, the arrow flew from the ground to the highest flight altitude in time t1 = t / 2 = 6/2 = 3 seconds. Then:

H = g * t1 ^ 2/2 = 10 * 3 ^ 2/2 = 5 * 3 ^ 2 = 5 * 9 = 45 meters.

S = 2 * H = 2 * 45 = 90 meters.

Answer: the maximum height of the arrow is 45 meters, the arrow has flown a path equal to 90 meters.