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?

1 Answer
Aug 5, 2017

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"" ")|)