Final answer:
To find the helicopter's acceleration, first calculate its mass by dividing the weight by gravity (22,807 N / 9.81 m/s²), resulting in approximately 2324 kg. The net force is the difference between the thrust and weight (46,196 N - 22,807 N), giving 23,389 N. The acceleration is then the net force divided by mass (23,389 N / 2324 kg), approximately 10.06 m/s².
Step-by-step explanation:
To calculate the acceleration of a helicopter that weighs 22,807 N and exerts an upward thrust force of 46,196 N, we first determine the mass of the helicopter using the gravitational force equation (weight = mass × gravity), with gravity being approximately 9.81 m/s². The mass (m) is calculated as:
m = weight / gravity
m = 22,807 N / 9.81 m/s²
m ≈ 2324 kg
Next, the net force (Fnet) acting on the helicopter is the difference between the upward thrust and the weight:
Fnet = thrust - weight
Fnet = 46,196 N - 22,807 N
Fnet = 23,389 N
Finally, we use Netwon's second law (F = ma) to find the acceleration (a):
a = Fnet / m
a = 23,389 N / 2324 kg
a ≈ 10.06 m/s²
The helicopter's acceleration is approximately 10.06 m/s² upwards.