A boat travels at a constant velocity from (1, 5) to (4, −3).

Question

A boat travels at a constant velocity from (1, 5) to (4, −3). Note that (1, 0) denotes a position of one
mile due east of the port and (0, 1) denotes a position of one mile due north of the port. The boat travels
at a speed of two miles per hour. Where will it be in 3 hours?

Answer 1

The direction from (1,5) to (4,-3) is given by the vector <4-1, -3-5>, or after simplifying: <3,-8>. This vector has length sqrt(9+64)=sqrt(73). Thus a unit vector in the same direction is <3/sqrt(73),-8/sqrt(73)>.

 

Traveling 2 mph for 3 hours, the boat will cover 6 miles. Thus, we can multiply our unit vector by 6, to obtain our travel vector: <18/sqrt(73),-48/sqrt(73)>, which is approximately <2.107,-5.618>. Adding that to our original position, we obtain the location: (1+2.107, 5-5.618), or (3.107, -0.618).