# the acceleration of the ladder extension on the firetruck

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 Ã˜ is 30Â° 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

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 Ã˜ is 30Â° 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

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