an aeroplane taxis onto the runway going at 10m/s if it can accelerate steadily at 3m/s^2 and its take off speed is 90m/s what length of runway will it need?
v = 10+at
so use that to find the time
s = 10t + 1/2 at^2
so use that time to calculate the distance needed
fiker
We are not given time (t)
Idon't know
I am student in grade 11th
To find the length of runway that the airplane will need, we can use the equations of motion from physics. The equation that relates distance, initial velocity, acceleration, and time is:
distance = initial velocity * time + (1/2) * acceleration * time^2
Here, we want to find the distance (length of runway), the initial velocity is 10 m/s, the acceleration is 3 m/s^2, and the takeoff speed is 90 m/s. We need to find the time it will take for the airplane to reach the takeoff speed.
Using the equation for final velocity, initial velocity, acceleration, and time:
final velocity = initial velocity + acceleration * time
We can rearrange this equation to solve for time:
time = (final velocity - initial velocity) / acceleration
Plugging in the values, we get:
time = (90 m/s - 10 m/s) / 3 m/s^2
= 80 m/s / 3 m/s^2
= 26.67 s
Now that we have the time, we can substitute it into the equation for distance to find the length of the runway:
distance = initial velocity * time + (1/2) * acceleration * time^2
= 10 m/s * 26.67 s + (1/2) * 3 m/s^2 * (26.67 s)^2
= 266.7 m + (1/2) * 3 m/s^2 * 712.2 s^2
= 266.7 m + 1068.3 m
= 1335 m
Therefore, the airplane will need a runway length of approximately 1335 meters to take off.