An aeroplane taxis onto runway going 10 meter per second.If it can accelerate steadily at 3 meter per second square and its take off speed is 90m\s what length of runway will it need?
the time it takes to get from 10 m/s to 90 m/s, increasing by 3 m/s every second, is t = (90-10)/3 = 80/3 s
Sow recall that s = 10t + 3/2 t^2
V^2 = Vo^2 + 2a*d.
90^2 = 10^2 + 6d,
d =
To determine the length of runway the airplane will need, we can use the equations of motion.
First, let's find the acceleration of the airplane. It is given that the airplane accelerates at a rate of 3 meters per second squared.
Next, we need to find the time it takes for the airplane to reach its takeoff speed. We can use the equation:
(vf - vi) = a * t
where vf is the final velocity (takeoff speed), vi is the initial velocity (taxiing speed), a is the acceleration, and t is the time.
Rearranging the equation to solve for time:
t = (vf - vi) / a
Substituting the given values:
t = (90 m/s - 10 m/s) / 3 m/s^2
t = 80 m/s / 3 m/s^2
t ≈ 26.67 s
Once we have the time it takes for the airplane to reach its takeoff speed, we can calculate the distance traveled during this time using the equation:
d = vi * t + 0.5 * a * t^2
where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time.
Substituting the values:
d = 10 m/s * 26.67 s + 0.5 * 3 m/s^2 * (26.67 s)^2
d = 266.7 m + 0.5 * 3 m/s^2 * 711.1 s^2
d = 266.7 m + 0.5 * 3 m/s^2 * 711.1 s^2
d = 266.7 m + 0.5 * 3 m/s^2 * 711.1 s^2
d = 266.7 m + 0.5 * 3 m/s^2 * 711.1 s^2
d = 266.7 m + 0.5 * 3 m/s^2 * 711.1 s^2
d = 266.7 m + 1066.65 m
d ≈ 1333.35 m
Therefore, the length of the runway needed for the airplane to take off is approximately 1333.35 meters.