If a projectile is shot at a velocity of #23 m/s# and an angle of #pi/12#, how far will the projectile travel before landing?
1 Answer
Explanation:
We're asked to find the horizontal range of the launched projectile with a known initial velocity.
To find this distance, we first must find the time
where

#Deltay# is the change in height of the projectile, in#"m"# , 
#v_(0y)# is the initial#y# velocity, in#"m"/"s"# . To find this, we must use the equation
#v_(0y) = v_0sinalpha# where
#v_0# is the initial speed (#23"m"/"s"# ), and
#alpha# is the initial launch angle (#pi/12# )Therefore, the initial
#y# velocity is
#v_(0y) = (23"m"/"s")sin(pi/12) = 5.95"m"/"s"#

#t# is the time, in#"s"# , and 
#g# is the acceleration due to gravity near Earth's surface,#9.8"m"/("s"^2)#
Plugging in
Now, to find how far horizontally it traveled, we use the equation
We must find the initial
The horizontal range is thus
rounded to