Answer to Question #126076 in Classical Mechanics for Amr Suliman

Question #126076

An airplane must reach a speed of 322 km/h to take off. If the runway is 500 m long, what is the minimum value of the acceleration that will allow the airplane to take off successfully?


1
Expert's answer
2020-07-13T11:42:50-0400

The relation between the trace of a body under acceleration with the last one is given by a formula:

"T = V_0t+\\frac{at^2}{2}" T - a trace, t - a time, "V_0, a" - the initial velocity and the acceleration

"V_0=0\\implies T = \\frac{at^2}{2}"(1)

The velocity "V" of the body in time "t":

"V = V_0 + at= at\\implies t = \\frac{V}{a}"(2)

Sibstitute(2) into (1):

"T = \\frac{V^2}{2a}\\implies a = \\frac{V^2}{2T}"

"a = \\frac{322*322}{2*0.5} = 103684\\frac{km}{h^2}"


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