A 12000 kg airplane launched by a catapult from an aircraft carrier is accelerated from 0 to 200 km/h in 3 s. (a) How many times the acceleration due to gravity is the airplane's acceleration?

g = 9.8 m/s

a = 2E5 m / 1.08E4 s^2 = 19 m/s^2

looks like about 2

g = 9.8 m/s^2

a = 2E5 m / 1.08E4 s^2 = 19 m/s^2

looks like about 2

V = 200,000m/3600s = 55.6 m/s = Final velocity.

V = Vo + a*t = 55.6
0 + a*3 = 55.6,
a = 18.52 m/s^2.

18.52m/s^2/9.8m/s^2 = 1.89 Times acceleration due to gravity.

To determine how many times the airplane's acceleration is compared to the acceleration due to gravity, we first need to find the values of both accelerations.

Acceleration due to gravity on Earth is approximately 9.8 m/s².

The given information provides the airplane's acceleration, but it is currently given in kilometers per hour. We need to convert it to meters per second to match the units of acceleration due to gravity (m/s²).

Step 1: Convert the airplane's initial and final speeds from km/h to m/s.

Given:
Initial speed (u) = 0 km/h
Final speed (v) = 200 km/h

To convert from km/h to m/s, we use the conversion factor: 1 km/h = 0.2778 m/s.

Initial speed (u) in m/s = 0 km/h * 0.2778 m/s = 0 m/s
Final speed (v) in m/s = 200 km/h * 0.2778 m/s = 55.56 m/s

Step 2: Calculate the airplane's acceleration.

Using the equation:

acceleration (a) = (v - u) / t,

where:
v = final speed,
u = initial speed,
t = time taken,

we can substitute the given values:

acceleration (a) = (55.56 m/s - 0 m/s) / 3 s
acceleration (a) = 55.56 m/s / 3 s
acceleration (a) = 18.52 m/s²

Step 3: Find how many times the airplane's acceleration is compared to the acceleration due to gravity.

Now that we have both accelerations, we can compare them:

number of times = airplane's acceleration / acceleration due to gravity

number of times = 18.52 m/s² / 9.8 m/s²
number of times ≈ 1.89

Therefore, the airplane's acceleration is approximately 1.89 times the acceleration due to gravity.