A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 205 mi/h in 3.00 s.
(a) Find the average acceleration of the plane.
(b) Assuming the acceleration is constant, find the distance the plane moves.
change mi/hr to m/s
a=changevelociyt/time
vf^2=2ad solve for distance
To find the average acceleration of the plane, we can use the formula:
acceleration = change in velocity / time
(a)
Given:
Initial velocity (u) = 0 (since the jet aircraft started from rest),
Final velocity (v) = 205 mi/h,
Time (t) = 3.00 s
Using the formula for average acceleration, we have:
acceleration = (v - u) / t
acceleration = (205 mi/h - 0 mi/h) / 3.00 s
acceleration = 205 mi/h / 3.00 s
acceleration ≈ 68.33 mi/h/s
So, the average acceleration of the plane is approximately 68.33 mi/h/s.
To find the distance the plane moves, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
(b)
Given:
Initial velocity (u) = 0 (since the jet aircraft started from rest),
Time (t) = 3.00 s,
Acceleration (a) ≈ 68.33 mi/h/s
Using the formula for distance, we have:
distance = 0 * 3.00 + (1/2) * 68.33 * (3.00)^2
distance = 0 + (1/2) * 68.33 * 9.00
distance = 0 + 31.67 * 9.00
distance ≈ 285.03 mi
So, the distance the plane moves is approximately 285.03 mi.
To find the average acceleration of the plane, we can use the formula:
Average acceleration = change in velocity / time
In this case, the change in velocity is the final velocity minus the initial velocity, and the time is given as 3.00 seconds. The final velocity is 205 mi/h, and since the plane starts from rest, the initial velocity is 0 mi/h.
(a) Average acceleration = (205 mi/h - 0 mi/h) / 3.00 s
= 205 mi/h / 3.00 s
To find the distance the plane moves, we can use the kinematic equation:
Distance = initial velocity * time + (1/2) * acceleration * time^2
Since we are given the initial velocity as 0 mi/h, the equation simplifies to:
Distance = (1/2) * acceleration * time^2
(b) Distance = (1/2) * (205 mi/h / 3.00 s) * (3.00 s)^2
= (1/2) * (205 mi/h) * (3.00 s)
Now we can calculate the answers:
(a) Average acceleration = (205 mi/h) / (3.00 s) ≈ 68.33 mi/h/s
(b) Distance = (1/2) * (205 mi/h) * (3.00 s) ≈ 307.5 mi
Therefore, the average acceleration of the plane is approximately 68.33 mi/h/s, and the distance it moves is approximately 307.5 miles.