Question

7marks t has a drag, F, given by F-a.w , where F is in newton's, W is the velocity of t with respect to the water (n m/5), and a -80 kg/m. The salil of the boat has a 10 m2 area and a drag coefficient of 1.2 when sailing before the wind (i.e., with a tailvi speed is 40 km/h. When saliling before the wind, calculate the Welodiy ofh boar s marke

Answer 1

Force on sail due to tailwind is given by:

$F_w = \frac{1}{2}c_d\, \rho \, v_w^2\, A$

Where $c_d$ = drag coefficient = 1.2
           $\rho$ = air density =1.225 kg/m³ [ International standard atmosphere value assuming sea level and 15^oC]
           $v_w$ = wind velocity = 40 km/h = (40 x 1000)/3600 m/s = 100/9 m/s
           A = area of sail = 10 m²

$\Rightarrow F_w = \frac{1}{2}\times 1.2\times 1.225\, kg/m^3\times \left( \frac{100}{9}\, m/s\right )^2\times10\, m^2$

            = 907.4074 N   [ $\because$ 1 N = 1 kg.m/s²

If this force makes the boat move with velocity W with respect t water, then

Where a=80 kg/m

$\Rightarrow W^2 = \frac{907.4074}{80}\: m^2/s^2 = 11.3426 \: m^2/s^2$

$\Rightarrow W = \sqrt{11.3426 \: m^2/s^2} = 3.3679 \, m/s = 12.1244 \, km/hr$ [Ans]