**1. Finding the speed of the rain with respect to the moving man:**

To find the speed of the rain with respect to the moving man, we need to consider the velocity of raindrops relative to the ground and the velocity of the man relative to the ground.

Let's assume the velocity of raindrops with respect to the ground is v_r and the velocity of the man with respect to the ground is v_m.

Now, we need to consider the angle at which the man is holding the umbrella. The angle of 30 degrees implies that the vertical component of the raindrops' velocity is equal to the horizontal component of the man's velocity.

Using trigonometry, we can find the vertical component of the raindrops' velocity (v_rv) and the horizontal component of the man's velocity (v_mh).

v_rv = v_r * sin(30)
v_mh = v_m

Since the man wants to avoid the rain, the vertical component of the raindrops' velocity should be equal to the vertical component of the man's velocity. This can be expressed as:

v_rv = v_m * cos(30)

Now, we can solve for the raindrops' velocity (v_r):

v_r * sin(30) = v_m * cos(30)
v_r = (v_m * cos(30)) / sin(30)

Therefore, the speed of the rain with respect to the moving man is (v_m * cos(30)) / sin(30).

**2. Finding the speed of the man with respect to the ground:**

To find the speed of the man with respect to the ground, we need to consider the velocity of the boat on which the man is running, and the velocity of the raindrops with respect to the ground.

Let's assume the velocity of the boat (and consequently, the man) with respect to the ground is v_b.

Now, we can find the speed of the man with respect to the ground by considering the vector addition of the velocities of the boat and the man relative to the ground.

The speed of the man with respect to the ground can be given as:

v_mg = v_b + v_m

Therefore, the speed of the man with respect to the ground is v_b + v_m.

In this case, we are given that the man is running at a velocity of 10 km/h on a straight boat, but we don't have information about the velocity of the boat itself. So, we cannot determine the exact speed of the man with respect to the ground without knowing the velocity of the boat.

However, based on the given information, we can state that the speed of the man with respect to the ground is at least 10 km/h, as he is running at that velocity on the boat.

Angle of rain is 30 degree
When the man runs with the speed of 10km/h he finds that rain falls vertically that means the horizontal component of rain was 10km/h then
Vx=10km/h
Now, vertical component
Vy=Vx/Vy= tan 30
Then, Vy=17.32km/h
Hope it helps