A boat is travelling with a speed of 27 km h - 1 due east. An observer is situated at 30 m south of the line of travel. The angular velocity of the boat relative to the observer in the position shown will be

Step-by-step solution

v = 27 km h - 1 = 7 . 5 m s - 1 Let us assume the location of the observer as the origin r → = 3 0 tan θ i ^ + 3 0 j ^ V → = d r → d t ; 7.5 = 3 0 sec 2 θ d θ d t i ^ 7.5 = 3 0 ω sec 2 θ ⇒ 7.5 = 3 0 ω sec 2 4 5 ° 7.5 3 0 × 2 = ω = 7.5 6 0 = 0.125 rad s - 1