Question

Two boats are heading away from shore. Boat 1 heads due north and is moving at a speed of 3.20 m/s relative to the shore. Relative to boat 1, boat 2 is moving due east at a speed of 4.30 m/s. A passenger on boat 2 runs due west across the deck at a speed of 5.40 m/s relative to boat 2. (a) What is the speed of boat 2 relative to the shore? (b) What is the speed of the passenger relative to boat 1? (c) What is the speed of the passenger relative to the shore?

Answer 1

Answer:

a. 5.360m/s

b. -1.1m/s

c. 3.38m/s

Explanation:

V1 = 3.20j

V2 = 4.30i

Vp = 5.4(-i)

= -5.40i

a. Speed of boat 2 relative to shore

= v1 + v2

= 3.2j + 4.3i

Magnitude = √3 2²+4.3²

= √28.73

= 5.360m/s

b. Speed of passenger relative to boat 1

V(p,1) = vp + v2

= -5.40i + 4.3i

= -1.1m/s

c. Speed of passenger relative to share

V(p,s) = vp + v(2,s)

= -5.4i + 4.30i +3.2j

= -1.1i + 3.2j

Take magnitude

= √-1.1²+3.2²

= √ 1.21 +10.24

= √11.45

= 3.38m/s