Acceleration and free fall problem

[cheerspens]

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?

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

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.

 

[w3390]

The first equation you have written (Vf^2 - Vi^2 = 2*a*x) should work. Assume the plane is starting from rest. This will give you all the variables except for the one you're looking for.

 

[kerimek]

This means that the minimum acceleration required for the jumbo jet to reach a speed of 300 km/hr in 2 km is 2250 km/hr^2. This is a very high acceleration, but it is necessary for the jet to successfully take off from the runway. It is important for pilots and engineers to consider this acceleration when designing and operating aircraft, as it can greatly impact the safety and efficiency of flights. Additionally, this problem highlights the concept of free fall, as the acceleration due to gravity (represented by the value of -9.8 in the equations) is a major factor in the jet's takeoff. Overall, this problem showcases the importance of understanding acceleration and its effects in real-world scenarios.