3.51
We want to find the x distance that projectile will travel depending on the angle that is was fired. In the x direction, in the absence of acceleration we find that
, or if we solve for t,
We can substitute this into what we know about y. In the
direction,
using the trigonometric identity that
Therefore, we can rewrite our equation as
We can substitute the x and y values for the point of the top of the
mountain since we are looking for the two parabolas that will
intersect that point. Then we can use the quadratic formula
to find two values
for . We find that
which correspond to and
.
Now we can use the range equation to find the x distance the
projectile travels.
from
the enemy ship, or 3065 - 2800 = 265m from shore.
from
the enemy ship, or 6276 - 2800 = 3476m from shore.
Therefore as long as the ship is closer than 265m to the shore or further than 3476m from the shore, it will be safe.