Problem Statement:
A person A with a mass of 50 kg rests on a swing of length 1 m, making an angle of 37° with the vertical. Another person B pushes person A, causing the swing to move to the other side at an angle of 53° with the vertical. We need to find the work done by person B, considering the acceleration due to gravity as 10 m/s^2.

Solution:

Let's break down the solution into steps:

Step 1: Determining the Initial Potential Energy:
The initial potential energy (U1) of person A can be calculated using the formula:

U1 = m * g * h

Where:
m = mass of person A = 50 kg
g = acceleration due to gravity = 10 m/s^2
h = vertical height = length of the swing * (1 - cos(angle with vertical))

Given:
Length of the swing = 1 m
Angle with vertical = 37°

Calculating the vertical height:
h = 1 * (1 - cos(37°))

Now, substituting the values in the formula:
U1 = 50 * 10 * [1 - cos(37°)]

Step 2: Determining the Final Potential Energy:
The final potential energy (U2) of person A can be calculated using the same formula as in Step 1, but with the new angle:

U2 = m * g * h'

Where:
Angle with vertical = 53°

Calculating the vertical height:
h' = 1 * (1 - cos(53°))

Now, substituting the values in the formula:
U2 = 50 * 10 * [1 - cos(53°)]

Step 3: Calculating the Work Done:
The work done by person B can be calculated as the difference in potential energy:

Work done = U2 - U1

Substituting the values of U1 and U2:
Work done = [50 * 10 * (1 - cos(53°))] - [50 * 10 * (1 - cos(37°))]

Simplifying the expression will give us the final answer.

Conclusion:
In conclusion, we can determine the work done by person B by calculating the difference in potential energy between the initial and final positions of person A on the swing. By substituting the given values and simplifying the expression, we can find the numerical value of the work done.