Question

A body is projected from the top of a tower of height of $32\text{m}$ with a velocity of $20\text{m/s}$ at an angle of ${37}^{\circ }$ below the horizontal. The time of flight of the projectile (in seconds) is

Answer 1

Time of flight only depends on the vertical component of velocity.
Initial vertical velocity $u_y=-20\sin {37}^{\circ }=-20\times \frac{3}{5}=-12\text{m/s}$
(taking upward direction as positive)

Displacement of the body when it reaches the ground $h=-32\text{m}$
Using second equation of motion,
$h=u_{y}t-\frac{1}{2}g{t}^2\Rightarrow -32=-12t-5t^2=0\Rightarrow 5t^2+20t-8t-32=0\Rightarrow 5t(t+4)-8(t+4)=0\Rightarrow t=\frac{8}{5}=1.6\text{s}$
(taking positive value of time)