A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 205 mi/h in 2.70 s.
(a) Find the average acceleration of the plane. (answer in m/s^2)
(b) Assuming the acceleration is constant, find the distance the plane moves. answer in (meters)
a. V = 205mi/h * 1600m/mi * 1h/3600s = 91.1 m/s.
V = Vo + a*t. V = 91.1 m/s, Vo = 0, t = 2.70 s. a = ?.
b. d = 0.5a*t^2. a = Value cal. in part "a", t = 2.70 s, d = ?.
To find the average acceleration of the plane, use the formula:
average acceleration = change in velocity / time
First, convert the speed of the plane from miles per hour (mi/h) to meters per second (m/s). We know that 1 mile = 1609.34 meters and 1 hour = 3600 seconds. Therefore:
205 mi/h * 1609.34 m/1 mi * 1 h/3600 s = 91.84 m/s
Now, plug the values into the formula:
average acceleration = (91.84 m/s - 0 m/s) / 2.70 s
Simplifying:
average acceleration = 34.01 m/s^2
So, the average acceleration of the plane is 34.01 m/s^2.
To find the distance the plane moves, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity is 0 m/s since the plane starts from rest. The time is 2.70 s, and the acceleration is 34.01 m/s^2.
Plugging in the values:
distance = 0 * 2.70 + (1/2) * 34.01 * (2.70)^2
Simplifying:
distance = 0 + 1/2 * 34.01 m/s^2 * (7.29 s^2)
distance = 124.14 meters
Therefore, the distance the plane moves is 124.14 meters.