RADIAL$/$TRANSVERSE COMPC NENTS: PROBLEM #$1$

Adapted from problem $11\mathrm{.}161$ in the textbook

Robots wihin telescoping arms are sometimes used to perform tasks

$($e$.$g$.,$ welding or placing screws$)$ where access may be difficult for

other robotic types. During a test run, a robot arm is programmed to

extend according to the relationship $r=t+2e^{-2t}$ and the arm

rotates according to the relationship $=3cos(3t)$ where r is in

inches, $$ is in radians, and t is in seconds. Determine the respective

magnitudes of the velocity and the acceleration of the screw that the

robot arm is holding $($i$.$e$.,$ point $A)$ at time $t=4s.$