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 is
(Take $g=10m/s^2$)

• A. $2\text{s}$
• B. $0.8\text{s}$
• C. $1.6\text{s}$
• D. $4\text{s}$

Answer 1

The correct option is C $1.6\text{s}$

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)