# Homework Help: Resultant velocity Question

1. Mar 22, 2012

### jacknjersey

1. The problem statement, all variables and given/known data

a boat heads north at 3.4 m s^-1 across a river that flows East at 1.6 m s ^-1.
1)Calculate the resultant velocity of the boat and the time taken to cross the river which is 180 m wide.
2)What is the distance travelled from its starting point when the boat reaches the far bank?
3)what direction must the boat steer in order to reach the bank directly opposite its starting point?

2. Relevant equations

j 3.4 m/s + i 1.6 m/s
52.94 seconds x 3.76 m/s
i sin theta + j cos theta

3. The attempt at a solution

1) j 3.4 m/s + i 1.6 m/s

j 3.76 m/s in a direction 25.2 degrees East of North. Time taken to cross is 180/3.4m/s which is 53 seconds.

2) distance travelled from starting point is 52.94s x 3.76 m/s = 199 m

3) to find direction:

i sin theata + j cos theta

3.4m/s (i sin theta + j cos theta) + 1.6i
where theta is the deviation from north. This requires 1.6 = =3.4 sin theta or theta - -28.1 degrees.

therefore the boat must head 28.1 degrees west of north.

How did I go?!

2. Mar 23, 2012

### Staff: Mentor

It looks right.

3. Mar 23, 2012

### ehild

It is perfect, except the typo in red. 1.6 = -3.4 sin theta .

ehild