Question

A boat 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.)

Answer 1

Answer:

$\textrm{Resultant velocity}\ =\ \sqrt{29}\ miles/hour$

along the direction 68.19° from north.

Step-by-step explanation:

Given,

• speed of the boat, u= 2 miles/hour along north

• speed of the river, v= 5 miles/ hour along east

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

$\vec{r}\ =\ 2\hat{i}+5\hat{j}$

Hence, the magnitude of resultant velocity can be written as

$r\ =\ \sqrt{2^2+5^2}$

  $=\ \sqrt{4+25}$

  $=\ \sqrt{29}$

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

And the direction of the boat can be given by,

$tan\theta\ =\ \dfrac{5}{2}$

$=>\ tan\theta\ =\ 2.5$

$=>\ \theta\ =\ tan^{-1}2.5$

                 = 68.19°

Hence, the resultant velocity of boat is $\sqrt{29}$ miles/hour along the direction making an angle 68.19° with the north.