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A block is initially held at rest at the bottom of a very long slide that is angled at 40 degrees with respect to the horizontal. There is no friction between the block and the slide. The block is then 'kicked' so that it begins up the slide with an initial speed equal to 3 m/s. Using only the principles of conservation of energy and geometry/trigonometry (do not use Free body diagrams or kinematic equations), determine the distance d that the block travels up the slide before it begins to come back down again. d.

A block is initially held at rest at the bottom of a very long slide that is angled at 40 degrees with respect to the horizontal. There is no friction between the block and the slide. The block is then 'kicked' so that it begins up the slide with an initial speed equal to 3 m/s. Using only the principles of conservation of energy and geometry/trigonometry (do not use Free body diagrams or kinematic equations), determine the distance d that the block travels up the slide before it begins to come back down again. d.

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**Physics Problem: Block on an Incline** A block is initially held at rest at the bottom of a very long slide that is angled at 40 degrees with respect to the horizontal. There is no friction between the block and the slide. The block is then 'kicked' so that it begins up the slide with an initial speed equal to 3 m/s. **Task:** Using only the principles of conservation of energy and geometry/trigonometry (do not use Free body diagrams or kinematic equations), determine the distance \(d\) that the block travels up the slide before it begins to come back down again. **Diagram Explanation:** - The image shows a right triangle with a block on its hypotenuse, representing the slide. - The slide is inclined at an angle \(\theta = 40^\circ\). - The block moves up the incline with an initial speed of 3 m/s. - The distance \(d\) is marked along the incline, which is the distance the block travels upward before stopping momentarily and descending again.
Transcribed Image Text:**Physics Problem: Block on an Incline** A block is initially held at rest at the bottom of a very long slide that is angled at 40 degrees with respect to the horizontal. There is no friction between the block and the slide. The block is then 'kicked' so that it begins up the slide with an initial speed equal to 3 m/s. **Task:** Using only the principles of conservation of energy and geometry/trigonometry (do not use Free body diagrams or kinematic equations), determine the distance \(d\) that the block travels up the slide before it begins to come back down again. **Diagram Explanation:** - The image shows a right triangle with a block on its hypotenuse, representing the slide. - The slide is inclined at an angle \(\theta = 40^\circ\). - The block moves up the incline with an initial speed of 3 m/s. - The distance \(d\) is marked along the incline, which is the distance the block travels upward before stopping momentarily and descending again.
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