Question

A projectile is shot at an angle of `pi/4` and a velocity of `5 m/s`. How far away will the projectile land?

Answer 1

If the projectile starts and ends at the same height (ie ground level), we can use the range formula, `Delta d_x=(v_i^2*sin(2 theta))/g`

Explanation:

A word of caution - the range formula is not universal. It is a derived formula using `Delta d_y=0`, in other words the start and end height are the same. If they are not the same (eg the projectile lands on a roof), a different technique must be used.

The range formula is

`Delta d_x=(v_i^2*sin(2 theta))/g`

where
`Delta d_x` is the horizontal distance (range)
`v_i` is the magnitude of the launch velocity
`theta` is the launch angle
`g` is the magnitude of the acceleration of gravity (usually 9.8, 9.81, or 10, depending on how the course is presented).

In this case,

`Delta d_x=(5^2*sin(2 pi/4))/g`