a large sphere is on a horizontal field on a sunny day. at a certain time the shadow reaches out a distance of 10 m from the poi
1 answer:
The radius of the sphere in meters is ,r =
Think about the angle the ground and the shadow make. Since the sun's beams are parallel, the angle created by the stick's shadow is also equal. Since the stick is 1 m high and its shadow is 2 m long, we know that the stick's angle is arctan 1/2. Therefore, by thinking of a right-angled triangle,
r/10 = tan [arctan(1/2)] = tan (1/2)
Since, tan (θ/2) = 1-cos(θ) / sin(θ)
we find that,
r/10 =
Hence, r =
So, the radius of the sphere in meters is ,r =
Learn more about radius (r) of the sphere here;
#SPJ4
You might be interested in
We can solve the problem by requiring the equilibrium of the forces and the equilibrium of torques.
1) Equilibrium of forces:
where
is the weight of the person
is the weight of the scaffold
Re-arranging, we can write the equation as
(1)
2) Equilibrium of torques:
where 3 m and 2 m are the distances of the forces from the center of mass of the scaffold.
Using
and replacing T1 with (1), we find
from which we find
And then, substituting T2 into (1), we find
1) Equilibrium of forces:
where
Re-arranging, we can write the equation as
2) Equilibrium of torques:
where 3 m and 2 m are the distances of the forces from the center of mass of the scaffold.
Using
from which we find
And then, substituting T2 into (1), we find
Answer:
x = -1.20 m
y = -1.12 m
Explanation:
as we know that four masses and their position is given as
5.0 kg (0, 0)
2.9 kg (0, 3.2)
4 kg (2.5, 0)
8.3 kg (x, y)
As we know that the formula of center of gravity is given as
Similarly for y direction we have