We're asked to find the time #t# when the projectile hits the ground with a given initial velocity and launch angle. In terms of physics, we need to find the time #t# when the height #y# is zero (there will technically be two times, one time was when the motion first started, and the second time is what we're trying to calculate--when it lands).
To find the time when it lands, we can use the equation
#Deltay = v_(0y)t - 1/2g t^2#
#Deltay# will be #0# (the change in its height), and we need to find the initial #y#-velocity, #v_(0y)#. We can find this by
#v_(0y) = v_0sinalpha = 18"m"/"s"sin((3pi)/4) = color(blue)(12.7"m"/"s"#
Plugging in our known values (#g = 9.80"m"/("s"^2)#), we have
#0 = (12.7"m"/"s")t - 1/2(9.80"m"/("s"^2))t^2#
#(4.90"m"/("s"^2))t^2 = (12.7"m"/"s")t#
#(4.90"m"/("s"^2))t = 12.7"m"/"s"#
#color(red)(t = 2.6"s"#
Thus, the projectile will land after #2.6"s"#.
