A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100.0 m/min relative to the water no matter which direction you point it. To cross this river, you start from a dock at point A on the south bank. There is a boat landing directly opposite at point B on the north bank, and also one at point C, 75.0 m downstream from B.

A) To reach point C at what bearing (angle north of west) must you aim your boat?

For this I got 83.5 deg N of W

B) Refer to part A. How long (t) will it take to cross the river?

For this I got 4.02 min

This is where I got stuck because I'm not sure how to do the last two parts...

C) Refer to part A. What distance (d, as measured by an observer on the ground) do you travel in m?

D) Refer to part A. What is the speed of your boat as measured by an observer standing on the river bank (=|VbG|) in m/min?

To solve parts C and D, we can break down the motion of the boat into horizontal and vertical components using trigonometry. Let's analyze the situation:

C) Distance Traveled:
Since we know the river is 400.0 m wide and you are crossing it downstream, the horizontal distance you need to travel (d) is the sum of the width of the river (400.0 m) and the horizontal distance you need to travel downstream from point B to point C (75.0 m).

Therefore, d = 400.0 m + 75.0 m = 475.0 m.

So, the distance you will travel is 475.0 m.

D) Speed of the Boat:
To find the speed of the boat as measured by an observer standing on the river bank, we need to consider the horizontal and vertical velocities separately.

The vertical velocity (Vv) of the boat remains constant at 30.0 m/min, as it is solely determined by the river's flow.

The horizontal velocity (Vh) of the boat relative to the ground can be found using the angle we calculated in part A. To do this, we can use trigonometry:

Vh = Vboat × cos(angle north of west)

Substituting the values:

Vh = 100.0 m/min × cos(83.5 deg)

Now we can calculate the speed of the boat as measured by an observer standing on the river bank (= VbG):

VbG = sqrt(Vh² + Vv²)

Substituting the values:

VbG = sqrt((100.0 m/min × cos(83.5 deg))² + (30.0 m/min)²)

Using a calculator, we can find:

VbG ≈ 101.4 m/min.

So, the speed of the boat as measured by an observer on the river bank is approximately 101.4 m/min.