an airplane has a takeoff speed of 80 meters per second which it reaches 35 seconds after starting from rest. What is the minimum length of the runway?
Start by calculating the acceleration of the plane as it moves from rest to take-off. It gets up to 80 m/s in 35 seconds, so its acceleration is 80/35 m/s^2.
Now you can just plug in the formula for distance travelled under acceleration = ut + 0.5at^2.
Initial velocity u is zero. We've worked out the acceleration, and we know that t=35sec. The rest is easy.
Well, I guess the airplane wasn't a fan of long walks on the runway!
To find the minimum length of the runway, we can use the formula:
Length = Speed × Time
So, the minimum length of the runway would be:
Length = 80 m/s × 35 s
That makes 2,800 meters! Although I must say, that's quite a stretch. The airplane better start doing some warm-up exercises before the takeoff!
To find the minimum length of the runway, we need to determine the distance traveled by the airplane during the takeoff.
We can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given:
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 80 m/s
Time (t) = 35 s
Since the airplane starts from rest, the initial velocity (u) is 0. Thus, we can simplify the formula to:
distance = (0.5 * acceleration * time^2)
Now, we can rearrange the formula to solve for the distance:
distance = (0.5 * acceleration * time^2)
Since we are looking for the minimum length of the runway, we can assume that the acceleration of the airplane remains constant throughout the takeoff.
To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Plugging in the given values:
acceleration = (80 m/s - 0 m/s) / 35 s
Now, solve for the acceleration:
acceleration = 80 m/s / 35 s
acceleration = 2.286 m/s^2
Now, substitute the values of acceleration and time into the formula for distance:
distance = 0.5 * 2.286 m/s^2 * (35 s)^2
Calculating this:
distance = 0.5 * 2.286 m/s^2 * 1225 s^2
distance = 2786.25 m
Therefore, the minimum length of the runway is 2786.25 meters.
To find the minimum length of the runway, we need to calculate the distance covered by the airplane during the takeoff. We can use the formula:
Distance = Average speed * Time
Average speed is calculated by taking the sum of the initial speed (0 m/s) and the final speed (80 m/s), and then dividing it by 2.
Let's plug the given values into the formula:
Average speed = (0 m/s + 80 m/s) / 2 = 40 m/s
Time = 35 seconds
Distance = 40 m/s * 35 seconds
Now we can solve for the distance covered during takeoff:
Distance = 1400 meters
Therefore, the minimum length of the runway must be at least 1400 meters for the airplane to take off safely.