Question

g A boat is anchored 2000 ft from shore anddirects its searchlight towards an automobile travelingdown the straight road. At the particular moment whenthe distance rfrom the searchlight to the automobile is3000 ft, the automobile has speed 80 ft/s and increasesits speed at a rate of 15 ft/s2 down the road.Find the required angular velocity and angularacceleration of the boat's searchlight to track the automobile at this instant.(Answers: 0.018 rad/s CCW, 0.004 rad/s2 CCW)

Answer 1

Step-by-step explanation:

The distance of searchlight will act as radius R and velocity of car may be supposed to be tangential velocity v . We are required to calculate angular velocity ω .

v = 80 ft /s

R = 3000 ft

ω = v / R

= 80 / 3000 = .027 rad / s

For angular acceleration the formula is

angular acceleration α = a / R

a is linear acceleration = 15 ft / s²

α = 15 / 3000 = .005 rad / s².