Question

A projectile is shot from the ground at a velocity of `8 m/s` and at an angle of `(7pi)/12`. How long will it take for the projectile to land?

Answer 1

`t = 1.58` `"s"`

Explanation:

We're asked to find the time `t` of an object's flight, given its initial velocity.

To do this, we recognize that when the object lands (assuming it launches and lands at the same height), its height `Deltay` will be `0`; we can use the equation

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

to find this time. For this equation,

• `Deltay` is the change in height (`0`)

• `v_0` is the initial speed (`8` `"m/s"`)

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

• `g` is the acceleration due to gravity near earth's surface (`9.81` `"m/s"^2`)

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

Plugging in known quantities:

`0 = (8color(white)(l)"m/s")sin((7pi)/12)t - 1/2(9.81color(white)(l)"m/s"^2)t^2`

`1/2(9.81color(white)(l)"m/s"^2)t^2 = (7.73color(white)(l)"m/s")t`

`(4.905color(white)(l)"m/s"^2)t = 7.73color(white)(l)"m/s"`

`t = (7.73color(white)(l)"m/s")/(4.905color(white)(l)"m/s"^2) = color(red)(1.58` `color(red)("s"`