A jet plane lands with a speed of 110 m/s and can decelerate uniformly at a maximum rate of 4.4 m/s^2 as it comes to rest.
Can this plane land at an airport where
the runway is 0.84 km long? Answer this by
calculating. Answer in units of k
To determine if the plane can land at the airport with a runway length of 0.84 km (840 m), we need to calculate the minimum distance required for the plane to come to a complete stop.
We know that the plane's initial speed is 110 m/s, and it can decelerate at a maximum rate of 4.4 m/s^2.
To find the minimum stopping distance, we can use the following formula:
d = (v^2 - u^2) / (2a)
where:
d = stopping distance
v = final velocity (0 m/s, as the plane comes to rest)
u = initial velocity (110 m/s)
a = acceleration/deceleration (-4.4 m/s^2, negative because it represents deceleration)
Plugging in the given values, we have:
d = (0^2 - 110^2) / (2*(-4.4))
Simplifying the equation, we calculate:
d = (-12100) / (-8.8)
d = 1375 m
The minimum stopping distance required for the plane to come to a complete stop is 1375 m.
Since the runway length is 840 m, which is less than the minimum stopping distance of 1375 m, the plane cannot land safely at this airport.