A steam catapult launches a jet aircraft (from rest) from the aircraft carrier John C. Stennis, giving it a speed of 160 mi/h in 2.40 s.
Find the average acceleration of the plane.
Assuming that the acceleration is constant, find the distance the plane moves.
160 miles per hour = 234.67 ft/s = 71.53 m/s is the velocity change during launch
I trust you know how to do the conversions.
Divide either of the last two numbers by the time interval, 2.40 s.
That will give you the acceleration in ft/s^2 or m/s^2 units, respectively.
To find the average acceleration of the plane, we can use the formula:
average acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (v0) is 0 mi/h, the final velocity (vf) is 160 mi/h, and the time (t) is 2.40 s, we can substitute these values into the formula:
average acceleration = (160 mi/h - 0 mi/h) / 2.40 s
Simplifying this expression, we get:
average acceleration = 160 mi/h / 2.40 s
To divide miles per hour (mi/h) by seconds (s), we need to convert mi/h to mi/s by dividing by 3600 (since there are 3600 seconds in an hour).
average acceleration = (160 mi/h / 3600 s) / 2.40 s
Now, we can calculate the average acceleration:
average acceleration = 0.017 mi/s / 2.40 s
average acceleration = 0.0071 mi/s²
Therefore, the average acceleration of the plane is 0.0071 mi/s².
To find the distance the plane moves, we can use the equation of motion:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the initial velocity (v0) is 0 mi/h, the time (t) is 2.40 s, and the acceleration (a) is 0.0071 mi/s², we can substitute these values into the equation:
distance = (0 mi/h * 2.40 s) + (0.5 * 0.0071 mi/s² * (2.40 s)^2)
Simplifying this expression, we get:
distance = 0 mi + 0.5 * 0.0071 mi/s² * (2.40 s)^2
distance = 0.027 mi/s² * 5.76 s²
distance = 0.1555 mi
Therefore, the distance the plane moves is approximately 0.1555 miles.