A plane traveling at 300.0 km/h attempts to land on a 500 m runway. The plane’s engines and brakes accelerate uniformly at –5.0 m/s2. Will the plane be able to land safely?
300 km/h is 83.3 meters per second. Divide that speed by the 5.0 deceleration rate to get the number of seconds needed to stop: 16.7 s
At an average speed of 83.3/2 m/s during that interval, the plane needs 694 meters to stop.
500 m is not enough runway.
To determine if the plane will be able to land safely, we need to calculate the stopping distance required for the plane to come to a complete stop before the end of the runway.
First, we need to find the deceleration of the plane's engines and brakes, which is given as -5.0 m/s^2.
Next, we can calculate the time it takes for the plane to stop using the formula:
time = final velocity / acceleration
Since the final velocity is 0 (since the plane is coming to a stop), we have:
time = 0 / (-5.0)
The time simplifies to 0 seconds.
Now, we need to calculate the distance traveled during this time. We can use the formula:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
The initial velocity is given as 300.0 km/h, which we need to convert to m/s:
initial velocity = (300.0 km/h) * (1000 m/km) / (3600 s/h)
Simplifying this expression gives us the initial velocity in m/s.
Now we can substitute the values into the equation:
distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Solving this equation will give us the distance traveled by the plane.
Finally, we compare the calculated distance to the length of the runway. If the distance is less than or equal to the length of the runway, the plane will be able to land safely. If the distance is greater than the length of the runway, the plane will not be able to stop in time and will not land safely.
By following these steps, we can determine whether the plane will be able to land safely on the given runway.