An archer defending a castle is on a 15.5 m high wall. He shoots the arrow straight down at 22.8 m/s. How much time does it take to reach the ground
To find the time it takes for the arrow to reach the ground, we can use the equation of motion for vertical free fall.
The equation is:
h = ut + (1/2)gt^2
where h is the initial height, u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Given:
h = 15.5 m (height of the wall)
u = 22.8 m/s (initial velocity)
We can rearrange the equation to solve for time (t):
15.5 = (1/2) * 9.8 * t^2
Multiplying both sides by 2:
31 = 9.8 * t^2
Dividing both sides by 9.8:
t^2 = 31 / 9.8
Taking the square root of both sides:
t = √(31 / 9.8)
Using a calculator, we can find the value of t:
t ≈ 1.78 seconds
Therefore, it takes approximately 1.78 seconds for the arrow to reach the ground.
using the "free fall" equation ... h = -1/2 g t^2 + vo t + ho
0 = -1/2 * 9.81 * t^2 - 15.5 t + 22.8
use the quadratic formula to find t