A basket is being dragged across a horizontal floor by two horizontal rope A and B which are inclined at 36 degree and 27 degree respectively with the direction in which the basket is moving.Rope A has a tension of 20Newton.Find the tension in rope B and the resultant force on the box.

To find the tension in rope B and the resultant force on the box, we can break down the forces acting on the basket.

Let's denote the tension in rope A as T_A and the tension in rope B as T_B.

1. Decompose the forces:
Since two ropes are acting on the basket, we need to break down the forces into their components. The components will be parallel and perpendicular to the direction of motion.

- Rope A: The tension T_A can be split into two components - T_A_parallel and T_A_perpendicular. The parallel component, T_A_parallel, will be responsible for moving the basket, while the perpendicular component, T_A_perpendicular, will cancel out with the corresponding component of rope B.

- Rope B: The tension T_B can also be broken down into two components - T_B_parallel and T_B_perpendicular. The parallel component, T_B_parallel, will also contribute to the motion of the basket, while the perpendicular component, T_B_perpendicular, will cancel out with the corresponding component of rope A.

2. Solve for the components:
Since we know the angle between the ropes and the horizontal floor, we can use trigonometric functions to calculate the components.

- T_A_parallel = T_A * cos(36°)
- T_A_perpendicular = T_A * sin(36°)
- T_B_parallel = T_B * cos(27°)
- T_B_perpendicular = T_B * sin(27°)

3. Apply Newton's second law:
The resultant force on the basket will be the vector sum of the parallel components of the tensions from both ropes.

- Resultant force (F_res) = T_A_parallel + T_B_parallel

4. Solve for the unknowns:
We can use the given information to solve for the tension in rope B (T_B) and the resultant force on the box (F_res).

- Given: T_A = 20 Newton
- Substitute the values in the equations and solve:
- Substitute T_A_parallel = T_A * cos(36°)
- Substitute T_B_parallel = T_B * cos(27°)
- Solve for T_B and F_res

By plugging in the known values of T_A, and using trigonometric functions to evaluate the parallel components, you can find the tension in rope B (T_B) and the resultant force on the box (F_res).