next up previous
Next: Homework Bookp.19, no.4 Up: No Title Previous: Probem 3.47

Problem 3.51

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

tex2html_wrap_inline475 , or if we solve for t,

tex2html_wrap_inline479

We can substitute this into what we know about y. In the tex2html_wrap_inline417 direction,

tex2html_wrap_inline483

tex2html_wrap_inline485

tex2html_wrap_inline487

using the trigonometric identity that

tex2html_wrap_inline489

Therefore, we can rewrite our equation as

tex2html_wrap_inline491

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 tex2html_wrap_inline493 . We find that

tex2html_wrap_inline495

which correspond to tex2html_wrap_inline497 and tex2html_wrap_inline499 . Now we can use the range equation to find the x distance the projectile travels.

tex2html_wrap_inline501 from the enemy ship, or 3065 - 2800 = 265m from shore.

tex2html_wrap_inline505 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.



Jason George Zeibel
Fri Sep 26 03:10:45 EDT 1997