The ladder of the fire truck rotates around the z axis with an angular velocity ω1 = 0.20 rad/s , which is increasing at 0.75 rad/s2 . At the same instant it is rotating upward at a constant rate ω2 = 0.65 rad/s .Determine the velocity of point A located at the top of the ladder at this instant. Enter the x, y, and z components of the velocity separated by commas. Determine the acceleration of point A located at the top of the ladder at this instant. Enter the x, y, and z components of the acceleration separated by commas. The image depicts a mechanical diagram of a fire truck with an extendable ladder. **Components and Annotations:**1. **Ladder:** The fire truck is equipped with a ladder that extends to a length of 40 feet. 2. **Angle of Elevation:** The ladder forms a 30° angle with the horizontal plane (y-axis). 3. **Angular Velocities:** - \( \omega_1 \): Rotational movement about the z-axis, represented by a circular arrow at the base of the ladder. - \( \omega_2 \): Rotational movement about the x-axis, represented by a circular arrow along the x direction.4. **Axes:** - The z-axis is vertical. - The x-axis is horizontal, pointing outward from the fire truck. - The y-axis is horizontal and perpendicular to the x-axis.5. **Truck Base:** The base of the ladder is mounted on a circular platform atop the fire truck, allowing for rotational movement. The truck is illustrated with two wheels for support.**Diagram Explanation:**This diagram provides a visual representation of the rotational dynamics involved when the ladder is being rotated and elevated. The integration of the angular velocities \( \omega_1 \) and \( \omega_2 \) demonstrates how the ladder can rotate about multiple axes, allowing it to be positioned accurately during operation.

Answered: The ladder of the fire truck rotates…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The ladder of the fire truck rotates around the z axis with an angular velocity ω1 = 0.20 rad/s , which is increasing at 0.75 rad/s2 . At the same instant it is rotating upward at a constant rate ω2 = 0.65 rad/s .

Determine the velocity of point A located at the top of the ladder at this instant. Enter the x, y, and z components of the velocity separated by commas.

Determine the acceleration of point A located at the top of the ladder at this instant. Enter the x, y, and z components of the acceleration separated by commas.

The image depicts a mechanical diagram of a fire truck with an extendable ladder.

**Components and Annotations:**

1. **Ladder:** The fire truck is equipped with a ladder that extends to a length of 40 feet.

2. **Angle of Elevation:** The ladder forms a 30° angle with the horizontal plane (y-axis).

3. **Angular Velocities:**
- \( \omega_1 \): Rotational movement about the z-axis, represented by a circular arrow at the base of the ladder.
- \( \omega_2 \): Rotational movement about the x-axis, represented by a circular arrow along the x direction.

4. **Axes:**
- The z-axis is vertical.
- The x-axis is horizontal, pointing outward from the fire truck.
- The y-axis is horizontal and perpendicular to the x-axis.

5. **Truck Base:** The base of the ladder is mounted on a circular platform atop the fire truck, allowing for rotational movement. The truck is illustrated with two wheels for support.

**Diagram Explanation:**
This diagram provides a visual representation of the rotational dynamics involved when the ladder is being rotated and elevated. The integration of the angular velocities \( \omega_1 \) and \( \omega_2 \) demonstrates how the ladder can rotate about multiple axes, allowing it to be positioned accurately during operation.

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