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maksim [4K]
3 years ago
7

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 r

ate 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.)
Mathematics
1 answer:
Ivahew [28]3 years ago
8 0

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.

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