gravitational force between two objects is given as
F = G m₁ m₂/r²
where m₁ = mass of first object , m₂ = mass of second object , r = distance between the two objects .
Initial case :
m₁ = m₂ = m
gravitational force between the objects is given as
F = G m²/r²
Final Case :
m₁ = m₂ = 3 m
new gravitational force between the objects is given as
F' = G (3m)²/r²
F' = 9 G m²/r²
F' = 9 F
hence the gravitational force between the two objects becomes 9 times.
Your average speed was
(100 m) / (13.8 s) = 7.25 m/s .
If you finished 0.001s ahead of him, then at your average speed, that corresponds to
(7.25 m/s) x (0.001 s) = 0.00725 m
That's 7.25 millimeters ... about 0.28 of an inch !
NOTE:. I think this is only valid if your speed was a constant ~7.25 m/s all the way.
That can only be happening if the mass mysteriously increased somehow. I'd like to know how in the world THAT happened.
Radioactive decay is given by:
N = No x e^(-λt)
We know that N/No has to be 0.05
λ = 0.15
0.05 = e^(-0.15t)
t = ln(0.05)/(-0.15)
t = 19.97 days
Answer:
the observed frequency will reduce but the wavelength will increase
Explanation:
As we know
fo = fs (v/(v-vs))
fo = observed frequency
vs = velocity of source
As per this equation,
When an observer moves away from the stationary source, the observed frequency reduces. Since the observer in the balloon is moving away from the source which itself is moving in opposite direction, the observed frequency will reduce.
Since wavelength = V/fs . The source frequency is unchanged but the velocity is increasing as it is moving in downward direction. Hence, the wavelength will increase
