A200-m-wide river flows due east at a uniform speed of 2.0 m/s. a boat with a speed of 8.0 m/s relative to the water leaves the south bank pointed in a direction 30° west of north. what are the (a) magnitude and (b) direction of the boat’s velocity relative to the ground? (c) how long does the boat take to cross the river?

Explanation:

Given

Width of river=200 m

Speed of river=2 m/s

Speed of Boat relative to river=8 m/s

Boat leaves the bank west of north

Therefore velocity of boat w.r.t ground

Magnitude of boat speed

For direction

w.r.t to west

to cross the river its north component will help so

time taken

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day