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.

the greatest force he can exert is HISWEIGHT*COEFFFRICTION or mu*mg

then the acceleration of the plane is

mu*g*manmass/planemass

oops...greatest acceleration is

mu*g*manmass/(manmass+planemass)

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

First, we need to calculate the maximum static friction force using the coefficient of static friction and the normal force acting on the man.

The normal force, N, acting on the man is equal to the force of gravity acting on the man's mass, which can be calculated using the formula: N = m x g
where m is the mass of the man and g is the acceleration due to gravity (approximately 9.8 m/s^2).

N = (95 kg)(9.8 m/s^2)
N = 931 N

Next, we can calculate the maximum static friction force, F_friction using the formula: F_friction = μ_s x N
where μ_s is the coefficient of static friction.

F_friction = (0.74)(931 N)
F_friction = 688.94 N

Now that we know the maximum static friction force, we can calculate the maximum acceleration, a_max, the man can give the airplane using Newton's second law of motion: F_net = m x a
where F_net is the net force acting on the airplane, m is the mass of the airplane and a is the acceleration.

Since the man is exerting the maximum static friction force on the airplane, the net force acting on the airplane is equal to the maximum static friction force.

F_net = F_friction = 688.94 N

The mass of the airplane, m_airplane is given as 122,000 kg.

Using F_net = m_airplane x a, we can now solve for a:

a = F_net / m_airplane
a = (688.94 N) / (122,000 kg)
a ≈ 0.00563 m/s^2

Therefore, the greatest acceleration the man can give the airplane is approximately 0.00563 m/s^2.