Question

A boat is travelling down stream in a river at 20 m/s south. A passenger on the boat walks toward the back of the boat at 10 m/s north. Relative to the ground, at what velocity is the passenger moving?
A) 10 m/s north
B) 10 m/s south
C) 30 m/s north
D) 30 m/s south

Answer 1

The question is unclear regarding the boat's velocity. Is it 20 m/s south relative to the water, or relative to the earth? (It is a river, after all...)

There's also the possibility that the boat's velocity relative to the river is 0. Take the south direction to be negative and north to be positive, and denote by $v_{A/B}$ the velocity of a body A relative to a body B. Under these conditions,

$v_{B/E}=v_{B/W}+v_{W/E}\iff-20\,\dfrac{\mathrm m}{\mathrm s}=0+-20\,\dfrac{\mathrm m}{\mathrm s}$

(B for boat, E for earth, W for water) so that the passenger's velocity relative to the earth is

$v_{P/E}=v_{P/B}+v_{B/W}+v_{W/E}$

(P for passenger)

$v_{P/E}=10\,\dfrac{\mathrm m}{\mathrm s}+0-20\,\dfrac{\mathrm m}{\mathrm s}=-10\,\dfrac{\mathrm m}{\mathrm s}$

or 10 m/s south.