Question

An archer defending a castle is on an 15.5 m high wall. He shoots an arrow straight down at 22.8 m/s. How much time does it take to reach the ground? (Unit = s) Watch your minus signs!​

Answer 1

Answer:

  about 602 milliseconds

Explanation:

The motion can be approximated by the equation ...

  y = -4.9t^2 -22.8t +15.5

where t is the time since the arrow was released, and y is the distance above the ground.

When y=0, the arrow has hit the ground.

Using the quadratic formula, we find ...

  t = (-(-22.8) ± √((-22.8)^2 -4(-4.9)(15.5)))/(2(-4.9))

  = (22.8 ± √823.64)/(-9.8)

The positive solution is ...

  t ≈ 0.60195193

It takes about 602 milliseconds for the arrow to reach the ground.