Solution: Quiz #6

Physics 12 - Quiz #6

Boats on a River

Solution:

a) The vector equation for the velocity of the boat with respect to the water is given by,

V_AW = V_AS + V_SW

where V_AS= 5.0 m/s with the course 30⁰ North of East

V_WS= 1.5 m/s in the direction of South

thus,

V_SW= 1.5 m/s in the direction of North

We can now draw the vector diagram the represents the vector equation.

We can now solve for V_AW.

b) The distance upstream is easily solved by determining the time of crossing using V_ASx and

then calculating vertical displacement using V_ASy.

c) The vector equation for the velocity of the boat with respect to the shore is given by,

V_BS = V_BW + V_WS

where V_BW= 2.5 m/s with a heading of 55⁰ South of East

V_WS= 1.5 m/s in the direction of South

The vector diagram should be drawn to aid in seeing the following calculations.

d) The time to cross the river is then simply calculated using the width of the river and the

x-component of V_BS.