Hypothetically a pebble rolls off the roof edge of Golden Eagle Arena and falls vertically. Just before it reaches the ground, the pebble's speed is 17 m/s. Neglect air resistance and determine the height of Golden Eagle Arena's roof edge.
To determine the height of the Golden Eagle Arena's roof edge, we can use the principles of kinematics, specifically the equation for the vertical displacement of an object in free fall:
Δy = V₀t + ½gt²
In this equation:
Δy represents the vertical displacement (height) of the object,
V₀ represents the initial vertical velocity (which is zero in this case, as the pebble drops from rest),
t represents the time taken for the pebble to fall, and
g represents the acceleration due to gravity (approximately 9.8 m/s²).
We can rearrange the equation to solve for Δy:
Δy = ½gt²
Given that the pebble's speed just before it reaches the ground is 17 m/s, we know that its final vertical velocity (V) is also 17 m/s (since it's moving vertically downward). We can use this information to find the time taken (t) by using the equation for final velocity:
V = V₀ + gt
17 m/s = 0 m/s + (9.8 m/s²)t
Solving for t, we find t ≈ 1.73 seconds.
Now, we can substitute this value of t back into the equation for vertical displacement:
Δy = ½gt²
Δy = ½(9.8 m/s²)(1.73 s)²
Calculating this, we find that the height of the Golden Eagle Arena's roof edge is approximately 14.3 meters.