For #2.
(A) The resultant velocity of the boat is the hypotenuse of a right triangle with the sides being the river and boat velocities.
The Pythagorean theorem: h^2 = a^2 + b^2
then you can use: soh cah toa to find any angles.
(B) The river velocity is not opposing the direction of travel, it increases the boats velocity from 2m/s to 2.5m/s
Answer:

Explanation:


If the sun considered as x=0 on the axis to put the center of the mass as a:

solve to r1


Now convert to coordinates centered on the center of mass. call the new coordinates x' and y' (we won't need y'). Now since in the sun centered coordinates the angular momentum was

where T = orbital period
then L'(x',y') = L(x) by conservation of angular momentum. So that means

Since
then

1.47x10^5 Joules
The gravitational potential energy will be the mass of the object, multiplied by the height upon which it can drop, multiplied by the local gravitational acceleration. And since it started at the top of a 60.0 meter hill, halfway will be at 30.0 meters. So
500 kg * 30.0 m * 9.8 m/s^2 = 147000 kg*m^2/s^ = 147000 Joules.
Using scientific notation and 3 significant figures gives 1.47x10^5 Joules.
The period T of a pendulum is given by:

where L is the length of the pendulum while

is the gravitational acceleration.
In the pendulum of the problem, one complete vibration takes exactly 0.200 s, this means its period is

. Using this data, we can solve the previous formula to find L: