A projectile is shot from the ground at a velocity of #12 m/s# at an angle of #pi/6#. How long will it take for the projectile to land?

1 Answer
May 16, 2016

Answer:

1.2s

Explanation:

Let the velocity of projection of the object be u with angle of projection #alpha# with the horizontal direction.
The vertical component of the velocity of projection is #usinalpha# and the horizontal component is #ucosalpha#

Now if the time of flight be T then the object will return to the ground after T sec and during this T sec its total vertical dosplacement h will be zero. So applying the equation of motion under gravity we canh write
#h=usinalphaxxT+1/2gT^2#
#=>0=uxxT-1/2xxgxxT^2#
#"where" g = "acceleration" "due to" gravity”#
#:.T=(2usinalpha)/g#
In our problem #u=12m/s and alpha=pi/6#

Hence #T=(2*12sin(pi/6))/9.8#
#=(2xx12xx1/2)/9.8=1.2s#