Answer:
In both cases the height is greater than 10.3 m
Explanation:
Pressure is defined by the relationship
P = F / A
in this case the force is the weight of the two gases
F = W = m g
If we use the definition of density
ρ = m / V
V = A h
m = ρ A h
we substitute
P = ρ g h
h = 
For this case the density of the gases is
ρ' = 0.9
h =
we calculate
ρ’= 0.9 \rho_{water}
h = 1 105 / (0.9 1000 9.8)
h = 11.3 m
ρ’= 0.8 \rho_{water}
h = 1 105 / (0.8 1000 9.8
h = 12.8 m
In both cases the height is greater than 10.3 m
The mass that must be added is 0.628 kg
Explanation:
The period of a mass-spring system is given by

where
m is the mass
k is the spring constant
For the initial mass-spring system in the problem, we have
m = 0.500 kg
T = 1.36 s
Solving for k, we find the spring constant:

In the second part, we want the period of the same system to be
T = 2.04 s
Therefore, the mass on the spring in this case must be

Therefore, the mass that must be added is

Learn more about period:
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Answer:
The equation of the time-dependent function of the position is 
(b) is correct option.
Explanation:
Given that,
Length = 12 cm
Mass = 200 g
Extend distance = 27 cm
Distance = 5 cm
Phase angle =0°
We need to calculate the spring constant
Using formula of restoring force





We need to calculate the time period
Using formula of time period

Put the value into the formula


At t = 0, the maximum displacement was 5 cm
So, The equation of the time-dependent function of the position

Put the value into the formula




Hence, The equation of the time-dependent function of the position is 
Answer:No
Explanation:
No
As the train is accelerating so train velocity will be more as compared to the ball and thus will cover more distance as compared to the ball.
When the ball is thrown upward with some velocity, it also possesses the train velocity at the time of throwing but as time passes velocity of train increases due to acceleration of the train. This causes the ball to fall behind the point of launch.
Remark
Always write down your givens and what you want to find. The formula you use for such questions will suggest itself if you do this.
Givens
a = 3.0 m/s^2
vi = 0 I presume that's that the question assumes.
vf = 33 m/s
You want d
Formula
vf^2 = vi^2 + 2*a*d
Solution
33^2 = 0^2 + 2 * 3 * d
1089 = 6*d
d = 1089/6
d = 181.5 meters