A40 kg girl and an 8.4 kg sled are on the surface of a frozen lake, 15 m apart. by means of a rope, the girl exerts a 5.2 n force on the sled, pulling it toward her.
(a) calculate the acceleration of the sled.
(b) calculate the acceleration of the girl.
(c) how far from the girl’s initial position do they meet, presuming a constant force? assume that no frictional forces act.

(a)

(b)

(c)

Explanation:

(a) According to Newton's second law, the acceleration of a body is directly proportional to the force exerted on it and inversely proportional to it's mass.

(b) According to Newton's third law, the force that the sled exerts on the girl is equal in magnitude but opposite in the direction of the force that the girl exerts on the sled:

(c) Using the kinematics equation:

For the girl, we have and . So:

For the sled, we have . So:

When they meet, the final positions are the same. So, equaling (1) and (2) and solving for t:

Now, we solve (1) for

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .