A projectile is shot at an angle of #pi/12 # and a velocity of #85 m/s#. How far away will the projectile land?
1 Answer
This is a standard problem about a parabolic trajectory.
Let us show that answer is ...
Explanation:
First of all, parabolic movement has two components: a horizontal (X axis) and a vertical (Y axis) one.

X axis follows a rectilinear, uniform motion , described by the equation:
#x = v_x cdot t#
where#x# is the distance far away from the point where the projectile is launched,#v_x# the forward speed, and#t# the time. 
Y axis follows a rectilinear, uniformly accelerated motion, described by the equation:
#y = v_{0y} \cdot t  frac 1 2 cdot g cdot t^2#
where#y# is the height of the projectile for every moment,#v_{0y}# the initial ascent speed,#g# the gravity acceleration#(g = 9,8 "m/s"^2)# and#t# the time.
The speed of projectile,
which can be calculated:
#v_x = v cdot cos theta# #v_y = v cdot sin theta#
where#theta# is the angle between trajectory and horizontal, and#v# is projectile speed.
We are going to use only 3 of the equations above:
Step 1 of 3:
Step 2 of 3: let us make
And now, we know that, at the end, the height of projectile is zero (because it lands on the floor), so
We choose
Step 3 of 3:
The projectile lands at 368.63 m from the origin.