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    the acceleration of the ladder extension on the firetruck

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    The firetruck us moving forward at a speed of 35 MPH and is decelerating at a rate of 10ft/sec.^2. Simultaneously, the ladder is being raised and extended.
    At the instant considered the angle Ø is 30° and is increasing at a rate of 10 degrees/sec . Also at this instant the extension b of the ladder is 5 ft and Vb = 2 feet / sec and ab = -1 ft/sec^2. Where Vb is the rate of extension of part b in ft/sec and ab is the acceleration of the extension of part b in ft/sec^2.

    Find the acceleration of point A with

    1. Respect to the truck
    2. Respect to the ground

    © BrainMass Inc. brainmass.com December 24, 2021, 7:13 pm ad1c9bdddf
    https://brainmass.com/physics/acceleration/acceleration-ladder-extension-firetruck-171976

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    The fire truck us moving forward at a speed of 35 MPH and is decelerating at a rate of 10ft/sec.^2. Simultaneously, the ladder is being raised and extended.
    At the instant considered the angle Ø is 30° and is increasing at a rate of 10 degrees/sec . Also at this instant the extension b of the ladder is 5 ft and Vb = 2 feet / sec and ab = -1 ft/sec^2. Where Vb is the rate of extension of part b in ft/sec and ab is the acceleration of the extension of part b in ft/sec^2.

    Find the acceleration of point A with

    1. Respect to the truck
    2. Respect to the ground

    Let's define the xyz coordinates as shown in the following figure

    B is the point on the truck. For the truck, its velocity and acceleration is to the right:

    Then we need to decompose them to the current coordinates:

    For the extension part b:

    The velocity is

    The acceleration is

    The angular velocity is counterclockwise and perpendicular to the xy-plane:

    The angular acceleration is 0 since angular velocity is constant.

    Using the equation to calculate the acceleration of point A with respect to ground:

    In the above equation:

    And

    Therefore, the acceleration of point A with respect to the ground is

    The acceleration of point A with respect to the truck is

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:13 pm ad1c9bdddf>
    https://brainmass.com/physics/acceleration/acceleration-ladder-extension-firetruck-171976

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