Answer:
The beam of light is moving at the peed of:
km/min
Given:
Distance from the isalnd, d = 3 km
No. of revolutions per minute, n = 4
Solution:
Angular velocity,
(1)
Now, in the right angle in the given fig.:

Now, differentiating both the sides w.r.t t:

Applying chain rule:


Now, using
and y = 1 in the above eqn, we get:

Also, using eqn (1),


Definition formula for momentum: P = mv
So P(A) = 0.45 * 50 = 22.5 kgm/s
P(B) = 0.45 * 80 = 36 kgm/s
P(C) = 0.45 * 25 = 11.25 kgm/s
B has the greatest momentum
Normal Force = 54 N
acceleration = 1.2 m/s^2
For Normal Force:
According to the force diagram, we can come up with the equation (all up and down forces):
10 sin 30 + Normal Force - 58.8 = 0
Normal Force = 53.8 N = 54 N
For acceleration:
According to the force diagram, we can come up with the equation (all left and right forces):
10 cos 30 - 1.5 = (6.0) (Acceleration)
Acceleration = 1.19 m/s^2 = 1.2 m/s^2