Question

Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.20 m/s relative to the shore. Relative to Boat 1, Boat 2 is moving 31.3° north of east at a speed of 1.61 m/s. A passenger on Boat 2 walks due east across the deck at a speed of 1.12 m/s relative to Boat 2. What is the speed of the passenger relative to the shore?

Answer 1

Take the velocities as into vector form, which means north as positive Y direction and east as the positive X direction Now, the velocity of the boat 1 relative to the shore is, (0, 3.20 The velocity of the boat 2 relative to boat 1 is. V21-1.61cos(31.3), 1.61sin (31.3) - {1.3757, 0.8364) The velocity of the boat 2 relative to the shore is, 12 (1.3757, 4.0364) Here, v, is the velocity of the boat 2. Thus, the velocity of the passenger with respect to boat 2 is, ' -(1.12 0) The velocity vector of the passenger with respect to the shore is, 3 2T32 (2.4957, 4.0364) Calculate the speed of the passenger relative to the shore v- /2.49572 +4.0364* 4.7456 4.75 m/s