To solve this question, we need to consider both the upward force provided by the helicopter's blades and the force of gravity acting on the helicopter.
First, let's calculate the weight of the helicopter using the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s². Therefore, the weight of the helicopter is:
Weight = 2500 kg × 9.8 m/s² = 24500 N
Now, let's find the net force acting on the helicopter:
Net force = upward force - weight
Upward force = 29 kN = 29000 N
Net force = 29000 N - 24500 N = 4500 N
Since the helicopter is accelerating upward at a constant rate, we can use Newton's second law of motion:
Net force = mass × acceleration
Rearranging the equation to solve for mass:
Mass = Net force / acceleration
Mass = 4500 N / 1.7 m/s² ≈ 2647 kg
Now that we have the mass of the helicopter, we can calculate the height it reaches. To do this, we need to consider conservation of energy. The initial kinetic energy is zero since the helicopter starts from rest. The final kinetic energy is also zero when the helicopter reaches its maximum height, so it only has gravitational potential energy.
Gravitational potential energy is given by the formula:
Potential energy = mass × gravity × height
Setting the potential energy equal to the gained energy (work done by the upward force of the blades), we have:
Potential energy = Upward force × distance
Since the upward force acts over a distance equal to the height, we can rewrite the equation as:
Mass × gravity × height = Upward force × height
Rearranging the equation to solve for height:
Height = (Upward force × height) / (Mass × gravity)
Height = (29000 N × height) / (2647 kg × 9.8 m/s²)
Simplifying the equation, we can substitute the diameter to calculate the height:
Height = (29000 N × height) / (2647 kg × 9.8 m/s²) = (29000 N × (2.6 m / 2)) / (2647 kg × 9.8 m/s²)
Height ≈ 2.98 m
Therefore, the helicopter's height at the moment its blades are providing an upward force of 29 kN is approximately 2.98 meters.