The searchlight on the boat anchored 2000 ft from shore is turned on the automobile, which is traveling along the straight road at a speed v = 50 ft/s

If the car is accelerating at 13 ft/s2 at the instant r = 3500 ft determine the required angular acceleration θ¨ of the light at this instant.

Express your answer using three significant figures.

θ¨ =

2.31×10−3

rad/s2