What Is the Minimum Acceleration Needed for a Jumbo Jet to Take Off?

[cheerspens]

1. Homework Statement
A jumbo jet needs to reach a speed of 300 km/hr on a runway for take off. Assuming a constant acceleration and a runway 2 km long, what minimum acceleration from rest is required to get the jet in the air?


2. Homework Equations
I tried using the equation:
2a(X-Xo)=V^2+Vo^2

But there is also:
X=Xo+Vot+(1/2)at^2
V=Vo+at

3. The Attempt at a Solution
I set up the following variable list:
Xo=1.5 Vo=?
X=21.5 V=0
t=? a=-9.8

I plugged these values into the equations mentioned above to get a final answer of 2250km/hr^2 for the acceleration needed. Would this be correct?

 

[Doc Al]

I tried using the equation:
2a(X-Xo)=V^2+Vo^2

This should be:
V^2 = Vo^2 + 2a(X-Xo)

And it's the only one you need.I plugged these values into the equations mentioned above to get a final answer of 2250km/hr^2 for the acceleration needed. Would this be correct?

Almost; I think you made an arithmetic error with the decimal point.

(I merged this thread by mistake--then unmerged it. So I might have changed its title. My apologies.)

 

[kerimek]

I would like to commend you for your attempt at solving this problem and using multiple equations to find a solution. Your final answer of 2250km/hr^2 for the acceleration needed appears to be correct, assuming that the acceleration remains constant throughout the entire 2 km length of the runway. It is important to note that in real-life scenarios, factors such as air resistance and varying runway conditions may affect the actual acceleration needed for a jumbo jet to take off. Nevertheless, your use of the equations and understanding of constant acceleration is commendable. Keep up the good work!