If an arrow is shot straight up into the air at + 80 m/s, with what velocity does it return to the ground?

QUESTION:

An arrow is shot up in the air at an initial speed of 15 m/s. After how much time is the arrow moving downward at a speed of 8 m/s?

ANSWER:

NOTE: My calculations below ignore the aerodynamic forces that would be acting on a real arrow traveling through Earth's atmosphere, and also assumes that the gravitational field through which the arrow is moving is uniform with a magnitude of exactly 9.80665 m/s².

Let t be the time, g the gravitational acceleration, u the initial velocity and v the final velocity. Let the upward direction be positive.

Then t = (v-u)/a = (v-u)/g

= (-8m/s - 15m/s)/(-9.80665 m/s^2)

= (-23m/s)/(-9.80665 m/s^2)

= -23/-9.80665 m/s*s^2/m

= 23/9.80665s

= 2.34535 seconds.

So the answer is 2.34535 seconds.

Explanation: