A projectile is fired from the bottom of incline plane of inclination ${37}^{\circ }$ at speed of $20$ m/s at an angle $\theta$ with incline plane as shown in figure. If time of flight is $3$ sec, then distance `AB` is $[g=10m/s^2]$

The correct option is D $21$ m
Considering $x$ coordinate along incline and $y$ coordinate perpendicular to incline.

Using 2nd equation of motion in $y$ direction and given time of flight $\Rightarrow$

$0=20sin\theta \times 3-\frac{1}{2}\times 10\times \frac{4}{5}\times 3^2\Rightarrow sin\theta =\frac{3}{5}$

For range `AB` we write equation of motion in `x` direction $\Rightarrow$

$AB=V_{0}cos\theta \times 3-\frac{1}{2}\times 10\times \frac{3}{5}\times 3^2$

$\Rightarrow AB=20\times 3\times \frac{4}{5}-27=21m$