Aboat heads north across a river at a rate of 2 miles per hour. if the current is flow a boat heads north across a river at a rate of 2 miles per hour. if the current is flowing east at a rate of 5 miles per hour, find the resultant velocity of the boat. (assume that east lies in the direction of the positive x-axis and north in the direction of the positive y-axis.)

along the direction 68.19° from north.

Step-by-step explanation:

Given,

Since, north and east are perpendicular to each other, so we can write the resultant velocity in vector form as,

Hence, the magnitude of resultant velocity can be written as

Hence, the magnitude of resultant vector is \sqrt{29} moles/hour.

And the direction of the boat can be given by,

                 = 68.19°

Hence, the resultant velocity of boat is miles/hour along the direction making an angle 68.19° with the north.