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

1 Answer
Jan 18, 2016

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#