Aircraft climbing upwards - When do they reach 3 km?

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SUMMARY

The discussion focuses on calculating the time taken for a jet aircraft to reach a height of 3 kilometers while climbing at a 60-degree angle. Key parameters include a thrust of 90 kN, an aircraft mass of 8 tonnes, and an average air resistance of 11 kN. To solve the problem, participants recommend resolving the forces acting on the aircraft, including thrust, air resistance, and weight, and applying Newton's Second Law (F=ma) to determine the vertical component of acceleration. The final calculation involves using the equation s=ut+0.5at² to find the time taken to reach the specified altitude.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Knowledge of vector resolution for forces and velocities
  • Familiarity with kinematic equations, specifically s=ut+0.5at²
  • Basic principles of aircraft dynamics and thrust-to-weight ratio
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  • Study vector resolution techniques for forces and velocities in physics
  • Learn more about kinematic equations and their applications in motion analysis
  • Research thrust-to-weight ratio and its impact on aircraft performance
  • Explore advanced dynamics of aircraft climbing and descent profiles
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Homework Statement



A jet aircrft climbs in a straight line at an atitude of 60 degrees to the horizontal the jet thrust amounts to 90 kn the mass of the aircraft is 8 tonne and the average air resistance amounts to 11kN calculate the time taken to reach a height of 3km if the speed at the start of the climb is 160km/h.

Homework Equations





The Attempt at a Solution



Any one help with what equations I use
 
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You're going to need to resolve forces, i recommend you use a diagram to help interpret it.

You have three forces you need to consider;

The propulsion force of the aircraft (the thrust).
The air resistance.
The weight.

The goal is to find the net force acting to move the aircraft upward, then using N2L (F=ma) you can find the vertical component of acceleration for the aircraft.

If we know the acceleration, the speed at the start (remember to also resolve the speed into vertical and horizontal components) and the height:

s=ut+0.5at^2 and solve for t.
 

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