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.
17/9.8=1.73s
x=vt-1/2at^2
y=(-17)(1.73)-1/2(9.8)(1.73)^2=14.7m
To determine the height of Golden Eagle Arena's roof edge, we can make use of the basic equations of motion for vertical motion under gravity.
The equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d) is:
vf^2 = vi^2 + 2ad
In this case, the final velocity of the pebble just before it reaches the ground is 17 m/s. Since the pebble is falling vertically under the influence of gravity, we can assume its initial velocity is 0 m/s, since it was dropped or rolled from rest. The acceleration due to gravity (a) can be approximated as -9.8 m/s^2 (taking into account that the downward direction is considered negative).
Plugging in these values into the equation, we get:
(17 m/s)^2 = (0 m/s)^2 + 2(-9.8 m/s^2)d
289 m^2/s^2 = 0 + (-19.6 m/s^2)d
Now, we can solve for the displacement (d), which represents the height of the roof edge:
d = 289 m^2/s^2 / (-19.6 m/s^2)
Simplifying the equation, we find:
d ≈ -14.7 meters
Since the displacement represents the vertical height and the downward direction is considered negative, we have a negative value for the displacement. In this case, it indicates that the height of Golden Eagle Arena's roof edge is approximately 14.7 meters.