an aeroplane taxis onto the runway going at 10m/s if it can accelerate steadly at 3m/s^2 & its take off spead is 90m/s what length of runway will it need?
find the time: v = v0 + at, so 10+3t = 90
Use that time for the distance: s = 10t + 3/2 t^2
To find the length of the runway the airplane will need for takeoff, we can use the equations of motion. The first step is to determine the time it takes for the airplane to reach its takeoff speed.
The initial velocity (u) of the airplane is 10m/s.
The acceleration (a) of the airplane is 3m/s^2.
The final velocity (v) of the airplane is 90m/s.
We can use the equation v = u + at, where t represents the time taken. Rearranging the equation to solve for t, we have t = (v - u) / a.
Plugging in the values, we get t = (90 - 10) / 3 = 80 / 3 seconds.
Next, we need to find the distance covered during this time interval. We can use the equation s = ut + (1/2)at^2, where s represents the distance covered.
Using the same initial velocity (u), acceleration (a), and time (t), we can calculate the distance covered:
s = (10 * (80/3)) + (1/2 * 3 * (80/3)^2)
= (800/3) + (1/2 * 3 * (6400/9)) (Simplifying)
= (800/3) + (3200/3) (Simplifying)
= 4000/3 meters
Therefore, the length of the runway required for the airplane to take off is 4000/3 meters or approximately 1333.33 meters.