A 6.4 ton military fighter must land on a flight strip. If the plane lands at a speed of 368 mph, and the coefficient of kinetic friction is 0.72 between the wheels and the ground. If the runway must be at least 150% as long as the shortest possible landing distance of the fighter, what is the shortest distance that the runway can be constructed?
HELP PLEASE I HAVE NO IDEA!
Convert mph to m/s. It is about 165m/s
mg*mu*distance=1/2 vi^2 * m
Notice mass m divides out.
distance=1/2*1/mu*vi^2
what is mu and vi? the last part 1/2*1/mu*vi^2
To find the shortest distance that the runway can be constructed, we need to calculate the landing distance of the military fighter.
The force of kinetic friction can be calculated using the formula:
Friction force = coefficient of kinetic friction * Normal force
The normal force is the gravitational force acting on the plane, which can be calculated using the formula:
Normal force = mass * gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s^2.
First, let's convert the mass of the fighter plane from tons to kilograms.
1 ton = 1000 kg
So, the mass of the plane is 6.4 tons * 1000 kg/ton = 6400 kg.
Next, let's calculate the normal force acting on the plane:
Normal force = 6400 kg * 9.8 m/s^2 = 62720 N
Now, we can calculate the force of kinetic friction:
Friction force = 0.72 * 62720 N = 45158.4 N
To calculate the deceleration (negative acceleration) of the plane, we can use Newton's second law:
Force = mass * acceleration
Rearranging the formula, we get:
Acceleration = Force / mass
Acceleration = 45158.4 N / 6400 kg = 7.06 m/s^2
Finally, we can calculate the landing distance using the equation of motion:
Distance = (initial_speed^2) / (2 * acceleration)
We need to convert the landing speed from mph to m/s.
1 mph = 0.44704 m/s
So, the landing speed is 368 mph * 0.44704 m/s/mph = 164.43952 m/s.
Plugging in the values:
Distance = (164.43952 m/s)^2 / (2 * 7.06 m/s^2)
Distance = 6712.38 m
Since the runway must be at least 150% as long as the shortest possible landing distance, we can calculate that by multiplying the landing distance by 1.5:
Shortest possible runway length = 6712.38 m * 1.5 = 10068.57 m
Therefore, the shortest distance that the runway can be constructed is approximately 10068.57 meters.