A man seeking to set a world record wants to tow a 122000-kg airplane along a runway by pulling horizontally on a cable attached to the airplane. The mass of the man is 95 kg, and the coefficient of static friction between his shoes and the runway is 0.74. What is the greatest acceleration the man can give the airplane? Assume that the airplane is on wheels that turn without any frictional resistance.

To find the greatest acceleration the man can give the airplane, we need to consider the maximum force of static friction between the man's shoes and the runway.

The maximum force of static friction (F_friction) can be calculated using the formula:

F_friction = coefficient of static friction * normal force

The normal force (F_normal) is equal to the weight of the man, which can be calculated using the formula:

F_normal = mass of the man * gravitational acceleration

The gravitational acceleration (g) is approximately 9.8 m/s² on Earth.

So, calculating the normal force:
F_normal = 95 kg * 9.8 m/s² = 931 N

Now we can calculate the maximum force of static friction:
F_friction = 0.74 * 931 N = 688.94 N

Since the man is pulling horizontally on the cable, the force he applies to the airplane is equal to the force of static friction. Therefore:

Force_applied = 688.94 N

To calculate the acceleration (a), we can use Newton's second law of motion:

Force_net = mass * acceleration

Since the mass of the airplane is given as 122,000 kg, the net force is equal to the applied force:

Force_net = Force_applied = 688.94 N

Now we can solve for acceleration:

acceleration = Force_net / mass
acceleration = 688.94 N / 122,000 kg

Calculating the acceleration:
acceleration = 0.00565 m/s²

Therefore, the greatest acceleration the man can give the airplane is approximately 0.00565 m/s².