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
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"" "))#