*14-28. The 10-lb box falls off the conveyor belt at 5-ft/s. If the coefficient of kinetic friction along AB is µg = 0.2, determine the distance x when the box falls into the cart.

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

The problem involves a 10-lb box that falls off a conveyor belt at 5 ft/s. With a coefficient of kinetic friction \(\mu_k = 0.2\) along the inclined plane \(AB\), the task is to determine the distance \(x\) when the box falls into the cart.

**Diagram Explanation:**

- The diagram shows a setup with a conveyor belt and an inclined plane that has a box moving downward.
- The initial height \(A\) is 15 ft above the ground.
- The inclined plane \(AB\) is shown with a 3-4-5 triangle, implying it has a specific slope.
- The inclined plane leads to a point \(B\), which is 30 ft above the ground.
- From point \(B\), the box follows a parabolic path to point \(C\), which is located 5 ft above the ground on the cart.
- The cart is positioned at a horizontal distance \(x\) from the base of the incline.

**Objective:**

Calculate the horizontal distance \(x\) where the box lands in the cart after sliding and falling off the inclined plane.
Transcribed Image Text:**Problem Statement:** The problem involves a 10-lb box that falls off a conveyor belt at 5 ft/s. With a coefficient of kinetic friction \(\mu_k = 0.2\) along the inclined plane \(AB\), the task is to determine the distance \(x\) when the box falls into the cart. **Diagram Explanation:** - The diagram shows a setup with a conveyor belt and an inclined plane that has a box moving downward. - The initial height \(A\) is 15 ft above the ground. - The inclined plane \(AB\) is shown with a 3-4-5 triangle, implying it has a specific slope. - The inclined plane leads to a point \(B\), which is 30 ft above the ground. - From point \(B\), the box follows a parabolic path to point \(C\), which is located 5 ft above the ground on the cart. - The cart is positioned at a horizontal distance \(x\) from the base of the incline. **Objective:** Calculate the horizontal distance \(x\) where the box lands in the cart after sliding and falling off the inclined plane.
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