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

Answer:

#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"" ")|)#