The motion of stone is subjected to gravitational and wind resistance of $0.82 m/sec^2,$ opposing the horizontal motion. Determine the time of flight of the stone.

$$u_x=u \cos 20=0.94u\hspace{1cm} u_y=u \sin θ=0.342u$$

$a_x=0.82 m/s^2 \hspace{1cm} a_y= -g= -9.81 m/s^2 \\ s_x=5 m \hspace{1cm} s_y= -2 m$

Horizontal $\hspace{1cm}$ vertical

$S_x=u_x t + \dfrac 12 a_x t^2 \hspace{1cm} S_y=U_x t=\dfrac 12 a_y t^2 \\ 5=0.94ut+ \dfrac 12×0.82×t^2 \hspace{1cm} -2=0.342 ut- \dfrac 12×9.81×t^2 \\ ut = \dfrac {5-0.41t^2}{0.94} ----(1)\hspace{1cm} ut=\dfrac {-2+4.905 t^2}{0.342} ----(2)$

From (1) and (2)

$\dfrac {5-0.41t^2}{0.94} = \dfrac {-2+4.905t^2}{0.342} \\ 5 \times 0.342 – 0.41 \times 0.34t^2 = -2 \times 0.94 +4.905 \times 0.94t^2 \\ 3.59 = 4.75 t^2 \\ t^2 = 0.7556 \\ t = 0.87 sec$

Time to flight of the stone is 0.87 sec.