Question

A boat is traveling west at 3.00 m/s across a river that is 68.5m wide. The current is 1.2m/s south.

A.Calculate the resultant velocity and direction of the boat

B. How long does it take to get across the river

C. How far down streak does the boat end up

Answer 1

Part a)

here boat is crossing the river at speed 3 m/s towards West

and the river current is flowing at 1.2 m/s towards South

So the net velocity of the boat is vector sum of river flow and boat velocity

Since the two velocity are perpendicular to each other so we will use pythagoras theorem to find the net velocity

$v_{net} = \sqrt{v_1^2 + v_2^2}$

$v_{net} = \sqrt{3^2 + 1.2^2}$

$v_{net} = 3.23 m/s$

direction of the net velocity is given as

$\theta = tan^{-1}\frac{v_1}{v_2}$

$\theta = tan^{-1}\frac{3}{1.2}$

$\theta = 68.2 degree$

so net velocity is 3.23 m/s in direction 68.2 degree West of south.

B) time taken to cross the river will be given as

$t = \frac{W}{v_1}$

$t = \frac{68.5}{3}$

$t = 22.83 s$

c) the distance covered by the boat in the direction of stream will be given as

$x = v_x * t$

$x = v_2 * t$

$x = 1.2* 22.83 = 27.4 m$

so it will cover a total distance of 27.4 m along the stream