A high performance jet, mass 2450 kg, has twin jet engines. Each jet engine can develop 25 000 N of thrust. (a) What is the maximum acceleration the jet c

Question

A high performance jet, mass 2450 kg, has twin jet engines. Each jet engine can develop 25 000 N of thrust.
(a) What is the maximum acceleration the jet can sustain in a vertical climb?
(b) How long would it take the jet to reach Mach 3 in horizontal flight starting from 50 m/s? Ignore wind resistance and use the freezing point of water for the air temperature.

Answer 1

I think this problem breaks down into several steps:

 

1.  Make a force diagram, or a free-body diagram (either one), labeling the vertical forces on this plane when it is in a vertical climb.  What forces act on it in the vertical direction in that case, and which way do they point, given that we are ignoring wind/air resistance?

 

2.  Use the force or free-body diagram to set up the expression for Newton's 2nd law, that F_net = ma, for the case of vertical climb as described.  You can make an expression for F_net from the diagram, and then set it equal to ma, and solve for the vertical acceleration in this case. This will answer question (a).

 

3.  Determine what the value for Mach 3 is under the given conditions.  Mach 3 is three times the speed of sound, so you have to determine the speed of sound if the air temperature is the freezing point of water.  You can use the speed of sound expression as a function of temperature from the tuning fork problem.

 

4.  Once you know the value for Mach 3, you know the final velocity the jet is to attain in its vertical climb, you know its initial velocity, and you know its (presumed constant) acceleration.  You can use this information and kinematics to solve to the time it takes to accelerate from 50 m/s to Mach 3 in these conditions.  This will answer question (b).

 

Hopefully, that will get you started.  If you want to flesh out steps, or confirm your through process, or check any intermediate or final results, just let me know!