Question

A projectile is shot at an angle of `pi/3` and a velocity of `11 m/s`. How far away will the projectile land?

Answer 1

It will land 10.7 m from its point of launch.

Explanation:

If you have the benefit of the following formula, the result is quickly obtained:

`R=(v_o^2)/(g) sin2theta`

`R=(11^2)/19.6 sin (pi/3) = 121/9.8 (0.866) = 10.7 m`

If you have not seen the above formula, it can be obtained through a (quite lengthy) calculation in which you use the equations of motion for a projectile, set up two equations in two unknowns, so that the time, `t` can be eliminated and solve for the distance `x` that the projectile moves horizontally. Many standard texts will show how this is done.

Wikipedia has the derivation here:

https://en.wikipedia.org/wiki/Range_of_a_projectile