A sailboat is pushed with a linear drag coefficient 83 g/m by wind blowing at a speed 2.97 m/s, while being slowed by a quadratic drag with the still water of 105 g/s. What is the cruising speed of the sailboat?

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Answer 1 · 2018-05-11T10:24:06

Let #v_c# be cruising speed of sailboat.
Velocity of wind relative to sailboat#=(2.97-v_c)\ ms^-1#

#F_"pushing"=83xx(2.97-v_c)\ gs^-1#

Given #F_"slowing"=105\ gs^-1#

As the sailboat is given to be cruising, net force must be #=0#. Therefore, equating both we get

#83xx(2.97-v_c)\ gs^-1=105\ gs^-1#

(Units of drag force are #N#. Given units are different. However, we are equating equal unit values, any constant multiplier gets taken care of)

#=>v_c=2.97-105/83#
#=>v_c=1.70\ ms^-1#