Question

A projectile is shot from the ground at a velocity of `84 m/s` and at an angle of `(7pi)/12`. How long will it take for the projectile to land?

Answer 1

`t = 16.5` `"s"`

Explanation:

We're asked to find the time it takes for a projectile to land, given its initial velocity.

To do this, we can use the kinematics equation

`ul(Deltay = v_0sinalpha_0t - 1/2g t^2`

where

• `Deltay` is the change in height (which is `0` when it lands)

• `v_0` is the initial speed (given as `84` `"m/s"`)

• `alpha_0` is the launch angle (given as `(7pi)/12`)

• `t` is the time (what we're trying to find)

• `g = 9.81color(white)(l)"m/s"^2`

Plugging in known values, we have

`0 = (84color(white)(l)"m/s")sin((7pi)/12)t - 1/2(9.81color(white)(l)"m/s"^2)t^2`

`(4.905color(white)(l)"m/s"^2)t^2 = (81.1color(white)(l)"m/s")t`

`(4.905color(white)(l)"m/s"^2)t = 81.1color(white)(l)"m/s"`

`t = color(red)(ulbar(|stackrel(" ")(" "16.5color(white)(l)"s"" ")|)`