Find the acceleration of $A$ at the instant shown. Indicate the direction with the sign based on the axes in the figure.

Express your answer to three significant figures in meters per second squared.

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Part B $-$ Acceleration of C

Find acceleration of $C,a_C,$ at the instant shown. Give your answer in component form.

Learning Goal:

To be able to use the equation for relative acceleration between two points

to find unknown linear accelerations and angular accelerations of

connected bodies.

Member ABC is controlled using a rack and pinion, which is connected at

$B.($The rack is the long, horizontal gear.$)$ The rack can only move

horizontally and the pinion does not translate. A block in a sleeve is

connected at A and allows movement only in the vertical direction.

Member ABC has a total length of $2\mathrm{.}30m$ and the distance between $A$

and $B$ is $1\mathrm{.}15m.$ When member ABC forms an angle of $=35\mathrm{.}0$ with

the rack, the acceleration of $B$ is $a_B=1\mathrm{.}55\frac{m}{s^2}$ and the velocity of the

block attached at $A$ is $v_A=2\mathrm{.}65\frac{m}{s}$ in the direction shown. Positive

angular velocity and acceleration are in the counterclockwise direction.

$($Figure $1)$

Express your two answers, separated by commas, to three significant figures in meters per second squared.

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Part C $-$ Acceleration of B

Find the acceleration of $B$ when the acceleration of $C$ is $a_C=4\mathrm{.}35i+3\mathrm{.}00j\frac{m}{s^2}$ and the acceleration of $A$ is $a_A=-3\mathrm{.}00j\frac{m}{s^2}.$ Mermber ABC makes an angle of $=21\mathrm{.}0$ at the instant

considered.

Express your answer to three significant figures in meters per second squared.

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$\sqrt[n]{},A,||$ vec

$a_B=i\frac{m}{s^2}$