Answer:
force becomes one - ninth
Explanation:
According to Coulomb's law in electrostatics, two charges can exert a force of attraction or repulsion on each other which is directly proportional to the product of two charges and inversely proportional to the square of distance between them.
Here both the charges remains same but the distance is variable.
So, we can say that
.... (1)
Where d be the distance between the tow charges
As the distance between two charges increases by factor of three, let the new force be F'.
.... (2)
Divide equation (2) by equation (1), we get


Thus, the force becomes one - ninth times the initial force.
Wee can use here kinematics
as we know that

for shorter tree we know that


now since we know that other tree is twice high
So height of other tree is y = 39.2 m
now again by above equation



so the time taken is 2.83 s
Answer:
<em>0.97c</em>
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Explanation:
From the relativistic equation for length contraction, we have
= 
where
is the final length of the object
is the original length of the object before contraction
β = 
where v is the speed of the object
c is the speed of light in free space = 3 x 10^8 m/s
The equation can be re-written as
/
= 
For the length to contract to one-fourth of the proper length, then
/
= 1/4
substituting into the equation, we'll have
1/4 = 
substituting for β, we'll have
1/4 = 
squaring both side of the equation, we'll have
1/16 = 1 - 
= 1 - 1/16
= 15/16
square root both sides of the equation, we have
v/c = 0.968
v = <em>0.97c</em>