A boat travels at 3.8 m/s and heads straight across a river 240m wide at an angle of 145'. The river flows at 1.6 m/s.

a. What is the boat's resultant speed with respect to the river bank?

b. How long does ti take the boat to cross the river?

c. How far downstream or upstream is the bot when it reaches the other side?

To solve this problem, we need to break down the boat's velocity into its horizontal and vertical components, find the resultant velocity, and then use this information to answer the given questions.

a. To find the boat's resultant speed with respect to the river bank, we need to find the horizontal component of the boat's velocity. The horizontal component is given by:

horizontal component = boat velocity * cos(angle)

Substituting the values into the formula:

horizontal component = 3.8 m/s * cos(145')

Now, calculate the horizontal component of the boat's velocity.

b. To calculate the time it takes for the boat to cross the river, we can use the formula:

time = distance / velocity

The distance in this case is the width of the river (240m), and the velocity is the horizontal component of the boat's velocity. Substitute the values and calculate the time.

c. To determine how far downstream or upstream the boat is when it reaches the other side, we need to find the vertical component of the boat's velocity. The vertical component is given by:

vertical component = boat velocity * sin(angle)

Substituting the values into the formula:

vertical component = 3.8 m/s * sin(145')

Now, calculate the vertical component of the boat's velocity.

Since the boat is moving perpendicular to the river's flow, the downstream or upstream distance will be the same as the vertical component of the velocity multiplied by the time calculated in part b.

Substitute the values and calculate the distance downstream or upstream.

By following these steps, you should be able to find the answers to all the given questions.