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?

Question

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!

Responses

Math - bobpursley, Tuesday, June 2, 2009 at 9:41pm
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

Math - Chelsea, Tuesday, June 2, 2009 at 9:49pm
what is mu and vi? the last part 1/2*1/mu*vi^2

Answer 1

Assume that the deceleration depends entirely on friction between wheels and runway, i.e. ignore turbine in reverse, and the slippage of the brake.

Then the standard kinematics equations apply:
v²-u² = 2aS

v=final velocity = 0 (at rest)
u=initial velocity = 368 mph=368*44/30 fps
a=kinetic frictional force devided by mass
=umg/m (m cancels out here)
=ug
=-0.72*32.3 f/s/s (negative for deceleration)
=-23.184 f/s/s

Substituting in values,

S=539.73²/(2*23.184)
=6286.6 ft

Apply a safety factor of 1.5 to the calculated length, so length of runway to be constructed
= 6286.6*1.5 ft.
= 9424 ft.

Answer 2

Thank you so much for explaining :)

Answer 3

In the equation given, "mu" represents the coefficient of kinetic friction and "vi" represents the initial velocity of the plane. To solve for the shortest distance, we need to find the values for these variables.

From the problem statement, we are given that the coefficient of kinetic friction is 0.72 and the initial velocity of the plane is 368 mph.

To convert mph to m/s, we can use the conversion factor 1 mph = 0.447 m/s.

So, the initial velocity of the plane in meters per second is:
vi = 368 mph * 0.447 m/s = 164.496 m/s (rounded to three decimal places)

Now, let's substitute the given values into the equation to find the shortest distance:
distance = 1/2 * 1/mu * vi^2

distance = 1/2 * 1/0.72 * (164.496^2)

Now, let's calculate the shortest distance using the equation:
distance = 1/2 * 1/0.72 * 27046.813

distance ≈ 18746.457 (rounded to three decimal places)

So, the shortest distance that the runway can be constructed is approximately 18746.457 meters.