A projectile is shot at an angle of #pi/12 # and a velocity of # 9 m/s#. How far away will the projectile land?
Distance to a landing spot is
Vector of velocity of a projectile should be represented as a sum of two vectors - horizontal and vertical components.
These components are:
While the vertical component brings the projectile up, after which it falls down, the horizontal component pulls it forward during the same time.
So, to find the distance to a landing spot, we need the time the projectile is flying.
On its way up the projectile's vertical component of the velocity is diminishing every second by
Therefore, with initial vertical component of
The same time is needed by the projectile to come back to earth, which brings the total time to go up and down to
During the same vertical component was dragging the projectile forward with a speed
So, the distance covered is