An F-18 with a weight of 22500 lbs lands on a carrier with a speed of 120 mph. If the run-out of the arresting cable is 160 ft, what is the planes acceleration in feet per second squared?
To find the plane's acceleration, we first need to calculate its deceleration during landing.
1. Convert the speed from mph to feet per second (fps):
Use the conversion factor: 1 mph = 1.46667 fps.
So, 120 mph * 1.46667 fps/mph = 175.9994 fps.
2. Calculate the stopping distance:
The stopping distance is given by the run-out of the arresting cable, which is 160 ft.
3. Use the following equation to calculate the deceleration:
v^2 = u^2 + 2ad
where:
v = final velocity (0 fps, as the plane comes to rest),
u = initial velocity (175.9994 fps),
a = acceleration (deceleration in this case, and what we're looking for),
d = stopping distance (160 ft).
Rearranging the equation gives:
a = (v^2 - u^2) / (2 * d)
Plugging in the values:
a = (0^2 - 175.9994^2) / (2 * 160)
Simplifying:
a = (-30957.21616) / 320
a ≈ -96.8037 fps^2.
Note: Since the plane is decelerating, the acceleration is negative, indicating a reduction in velocity.