Answer:
dart's speed is 11.77 m/s
Explanation:
given data
mass of the gun m = 355 gram = 0.355 kg
height = 18.3 centimeters = 0.183 m
dart = 57.0 gram = 0.057 kg
to find out
dart's speed
solution
we apply here law of conservation of energy that is express as
mgh = 0.5 × m × v² ...........1
so speed of gun will be here as
V =
..................2
V =
V = 1.89 m/s
and
now we find speed of dart by use law of conservation of momentum that is
M×V = m×v ...............3
so speed of the dart is
v = 
v = 
v = 11.77 m/s
so dart's speed is 11.77 m/s
Potential energy is stored energy because it has the potential to do something which laters turns into kinetic energy which is the moving energy.
(a) The distance will be more than 2.0 meters.
In fact, you starts your fall after your friend has already fallen 2.0 meters. This means that your friend has already accelerated for a while, therefore his velocity will be greater than yours. But this statement will be actually true for the entire fall, since you has some delay, therefore when your friend will hit the water, the separation between you and him will be greater than the initial separation of 2.0 meters.
b) First of all we need to calculate the height of the bridge with respect to the water. We know that you take 1.6 s to fall down, therefore we can use the following equation:

We know that your friend will take 1.6 s to falls down. Instead, you start your jump after he has already fallen 2.0 m, therefore after a time given by the equation:

Using S=2.0 m,

So we know that you start your fall 0.64 s after your friend. Therefore, now we can find how much did you fall between the moment you started your fall (0.64 s) and the moment your friend hits the water (1.6 s). Using

we find

So, when your friend hits the water, you just covered 4.52 m, while he already covered 12.56 m. Therefore, the separation between you and your friend is more than 2 meters.
The internal energy of the gas is 49,200 J
Explanation:
The internal energy of a diatomic gas, such as
, is given by

where
n is the number of moles
R is the gas constant
T is the absolute temperature of the gas
For the gas in this problem, we have:
n = 4.50 (number of moles)
R = 8.31 J/(mol·K) (gas constant)
(absolute temperature)
Substituting, we find:

Learn more about ideal gases:
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As frequency decreases , the wavelength will increase !!
frequency= speed of light ÷ wavelength
( inverse relationship )