A jet plane lands with a velocity of 100 m/s and can accelerate at a maximum rate of -5.0 m/s2 as it come to rest. Can this plane land at an airport where the runway is 0.80 km long?
s= [(v(fin) ² -v(init)²]/2•a=( 0-10000)/2•(-5)= 1000 m
This jet needs the plane land of the length 1000 m
s= [(v(fin) ² -v(init)²]/2•a=( 0-10000)/2•(-5)= 1000 m
This jet needs the plane land of the length 1000 m
To determine if the plane can land safely on the runway, we need to calculate the distance it needs to stop within. We know the initial velocity (v = 100 m/s), the maximum acceleration (a = -5.0 m/s²), and the length of the runway (s = 0.80 km = 800 m).
Let's use the equation of motion to solve for the distance the plane will travel before coming to rest:
v² = u² + 2as
Where:
v = final velocity (0 m/s, since the plane comes to rest)
u = initial velocity (100 m/s)
a = acceleration (-5.0 m/s²)
s = distance
Plugging the values into the equation:
0² = 100² + 2(-5.0)s
0 = 10,000 - 10s
10s = 10,000
s = 10,000 / 10
s = 1,000 m
The distance required for the plane to stop completely is 1,000 m.
Since the runway is only 800 m long, the plane cannot land safely without potentially overrunning the runway. It would need a longer runway to land.
To determine if the jet plane can land at the airport, we need to calculate the distance it takes for the plane to come to a complete stop.
Let's break down the steps:
1. Convert the velocity from m/s to km/h:
Velocity = 100 m/s = (100 m/s) x (3600 s/h) / (1000 m/km) = 360 km/h
2. Convert the runway length from km to meters:
Runway Length = 0.80 km = 0.80 km x (1000 m/km) = 800 m
3. Use the equation of motion to calculate the distance the plane takes to decelerate and stop:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the plane comes to rest)
u = initial velocity (360 km/h)
a = acceleration (-5.0 m/s^2)
s = distance
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
s = (0^2 - (360 km/h)^2) / (2 x -5.0 m/s^2)
s = (-129,600,000 m^2/h^2) / (-10 m/s^2)
s = 12,960,000 m
4. Compare the calculated distance (12,960,000 m) to the runway length (800 m).
Since the calculated distance is significantly longer than the runway length, the plane cannot land safely at this airport.
In conclusion, the jet plane cannot land at an airport with a runway that is 0.80 km long.