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?

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To solve this problem, we can use vector addition and trigonometry. Here's how you can find the answers to each question:

a. First, we need to find the horizontal and vertical components of the boat's velocity. The horizontal component is given by the boat's speed (3.8 m/s) times the cosine of the angle (145°) since it is heading straight across the river. The vertical component is zero since the boat is not moving up or down the river.

Horizontal component of velocity = 3.8 m/s * cos(145°) ≈ -2.011 m/s (negative sign indicates opposite direction of river flow)
Vertical component of velocity = 0 m/s

The resultant speed with respect to the river bank is the magnitude of the resultant velocity, which can be found using the Pythagorean theorem:

Resultant speed = sqrt((horizontal component of velocity)^2 + (vertical component of velocity)^2)
= sqrt((-2.011 m/s)^2 + (0 m/s)^2)
≈ 2.011 m/s

Therefore, the boat's resultant speed with respect to the river bank is approximately 2.011 m/s.

b. To find the time it takes for the boat to cross the river, we can use the formula: time = distance / speed. The distance to be covered is the width of the river (240 m) and the speed is the resultant speed (2.011 m/s).

Time = 240 m / 2.011 m/s ≈ 119.42 seconds

Therefore, it takes the boat approximately 119.42 seconds to cross the river.

c. To find how far downstream or upstream the boat is when it reaches the other side, we need to calculate the horizontal displacement. This can be found by multiplying the boat's horizontal speed by the time taken to cross the river.

Horizontal displacement = (horizontal component of velocity) * time
= (-2.011 m/s) * 119.42 s
≈ -240.06 m

Since the negative sign indicates the opposite direction of the river's flow, the boat is approximately 240.06 meters upstream when it reaches the other side.

Therefore, the boat is approximately 240.06 meters upstream when it reaches the other side.