Question

Two boats are heading away from shore. Boat 1 heads due north at a speed of 2.97 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 28.3° north of east at a speed of 1.66 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.18 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?

Answer 1

Solution :-

Let the direction be as shown below:

Y axis E Xaxis

Vb1,s (velocity of boat 1 with respect to shore) = 2.97 j

Vb2,b1 (velocity of boat 2 with respect to boat 1)= 1.66cos 28.3 i + 1.66sin 28.3 j
= 1.46 i + 0.79 j

Vp,b2 (velocity of passenger with respect to boat2) = 1.18 i

Vp,s = Vp,b2 + Vb2,b1 + Vb1,s
= 1.18 i + 1.46 i + 0.79 j + 2.97 j
= 2.64 i + 3.76 j

speed = Magnitude of velocity= sqrt (2.64^2 + 3.76^2) = 4.64 m/s