How long will an arrow be in flight if it is fired vertically upward from a bow at a speed of 40 m / s?

Initial data: V01 (initial speed of the boom) = 40 m / s; V1 = V02 = 0 m / s (speed at maximum height).

Constants: g (acceleration of gravity) = 10 m / s ^ 2 = a (acceleration of an arrow).

1) Boom lifting time: V1 = V01 – g * t1 and t1 = V01 / g = 40/10 = 4 s.

2) Lifting height: Н = V0 * t1 – g * t1 ^ 2/2 = 40 * 4 – 10 * 4 ^ 2/2 = 80 m.

3) Arrow fall time (free fall): Н = g * t2 ^ 2/2 and t2 = √ (2H / g) = √ (2 * 80/10) = 4 s.

4) Time in flight: t = t1 + t2 = 4 + 4 = 8 s.