Aircraft climbing upwards - When do they reach 3 km?

[speedy46]

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

 

[astrorob]

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.