A 7500 kg plane is launched from an aircraft carrier in 2.2 seconds, what is the planes acceleration? what is its velocity?
You have omitted one necessary piece of information such as the launching force, or the distance over which the acceleration occurs.
With what you have provided, an infinite number of answers are possible.
What does that mean?
To calculate the acceleration of the plane, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, we need to rearrange the formula to solve for acceleration.
Given:
Mass of the plane (m) = 7500 kg
We can assume that the force applied is equal to the weight of the plane (mg), where g is the acceleration due to gravity (approximately 9.8 m/s²).
Weight of the plane (mg) = (7500 kg) x (9.8 m/s²)
Next, we need to determine the time it takes for the plane to launch. In this case, it is given as 2.2 seconds.
Using the formula for acceleration (a = Δv/Δt), where Δv represents change in velocity and Δt represents change in time, we can rearrange it to solve for acceleration.
Δv = v - u, where v is the final velocity and u is the initial velocity.
Given:
Δt = 2.2 seconds
u (initial velocity) = 0 m/s (plane starts from rest)
Now, to calculate the acceleration of the plane:
Acceleration (a) = (final velocity - initial velocity) / time
Since the plane starts from rest, the initial velocity (u) is 0 m/s. Thus, the formula simplifies to:
Acceleration (a) = final velocity / time
Solving for acceleration:
Acceleration (a) = Δv / Δt
Acceleration (a) = v / Δt
To find the final velocity (v), we can rearrange the formula for acceleration:
v = a * Δt
Now we can substitute the given values into the formulas to find the acceleration and velocity of the plane.
Acceleration (a) = (7500 kg * 9.8 m/s²) / 2.2 s
Acceleration (a) = 33818.18 m/s² (rounded to two decimal places)
The acceleration of the plane is approximately 33818.18 m/s².
To find the final velocity (v):
v = (33818.18 m/s²) * (2.2 s)
v = 74399.99 m/s (rounded to two decimal places)
The final velocity (v) of the plane is approximately 74399.99 m/s.