Question

Длина разбега самолета равняется 1215 метров а скорость необходимая для отрыва от земли 270 километров час Найти ускорение и время разбега

Answer 1

Для начала переведем скорость самолета в СИ: 270 км/ч = 75 м/с.
Начальная скорость самолета равна 0, следовательно,
$S= \frac{v}{2} t$, где S =1215 м, v = 75 м/с, t -- время разбега.
$t= \frac{2S}{v} = \frac{2*1215}{75} =32.4 c$
А ускорение найдем из соотношения: $S= \frac{at^{2} }{2}$
$a= \frac{2S}{t^{2} } = \frac{2*1215}{32.4^{2} }=2,3$ м/с^2

Answer 2

Calculation of Acceleration and Takeoff Time

To find the acceleration and takeoff time of an airplane, we can use the given information: the length of the runway (1215 meters) and the necessary takeoff speed (270 kilometers per hour).

The formula to calculate acceleration is:

Acceleration (a) = (Final Velocity^2 - Initial Velocity^2) / (2 * Distance)

Given that the initial velocity is 0 (since the airplane starts from rest), the formula simplifies to:

Acceleration (a) = Final Velocity^2 / (2 * Distance)

We can convert the given takeoff speed from kilometers per hour to meters per second by dividing it by 3.6:

Final Velocity = 270 km/h ÷ 3.6 = 75 m/s

Substituting the values into the formula, we get:

Acceleration (a) = (75^2) / (2 * 1215) = 5625 / 2430 = 2.31 m/s^2.

To find the takeoff time, we can use the formula:

Time (t) = Final Velocity / Acceleration

Substituting the values, we get:

Time (t) = 75 / 2.31 = 32.47 seconds.

Therefore, the acceleration of the airplane is approximately 2.31 m/s^2, and the takeoff time is approximately 32.47 seconds.

Please note that these calculations assume constant acceleration and do not take into account other factors such as air resistance or variations in acceleration during the takeoff process.