Question

A projectile is shot from the ground at a velocity of `7 m/s` and at an angle of `(7pi)/12`. How long will it take for the projectile to land?

Answer 1

Let the velocity of projection of the projectile 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 displacement h will be zero. So applying the equation of motion under gravity we can write
`h=usinalphaxxT+1/2gT^2`

`=>0=uxxT-1/2xxgxxT^2`

`"where "g = "acceleration due to gravity"`

`:.T=(2usinalpha)/g`

In the given problem

`u=7"m/s" and alpha=(7pi)/12 " "g=9.8m/s^2`

`T=(2xx7xxsin((7pi)/12))/9.8=1.38s`