Answer:
5.5 m/s
Explanation:
Assuming the bottle is initially stationary, we can write the law of conservation of momentum as follows:

where
is the mass of the ball
is the initial velocity of the ball
is the mass of the bottle
is the final velocity of the bottle
is the final velocity of the ball
Solving for
,

(a) 1800 N
The equation of the forces along the vertical direction is:

where
is the component of the applied force along the vertical direction
N is the normal force on the sled
mg is the weight of the sled
Substituting:
F = 1210 N
m = 246 kg

We find N:

(b) 0.580
The equation of the forces along the horizontal direction is:

where
is the horizontal component of the push applied by the mule
is the static frictional force
Substituting:
F = 1210 N
N = 1800 N

We find
, the coefficient of static friction:

(c) 522 N
In this case, the force exerted by the mule is

So now the equation of the forces along the horizontal direction can be written as

where

and
is the new frictional force, which is different from part (b) (because the value of the force of friction ranges from zero to the maximum value
, depending on how much force is applied in the opposite direction)
Solving the equation,

Newton's second law states that the force applied to an object is equal to the product between the mass m of the object and its acceleration a:

Using

and

, we can find the value of the force applied to the roller-blade to obtain this acceleration:
It's a plain, not a lever