Suppose you are swimming underwater in a lake and a sound is made 1,000 meters away from you. How long would it take for the sou
1 answer:
Answer:
0.667 s; faster in the ocean
Explanation:
Since the sound wave travels with a uniform motion (= at constant velocity), the time it takes to reach your ear will be given by the formula
where
d is the distance it has to cover
v is the speed of the sound wave
Here we have
d = 1000 m is the distance
v = 1500 m/s is the approximate speed of sound in fresh water
Substituting,
We also want to compare the time if you are swimming in the ocean.
In the ocean, due to the higher density of the water (because of the presence of the salt), the speed of sound is slightly larger, in fact it is:
Therefore, the time taken in this case will be:
Therefore, the sound will reach your ear a bit faster.
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Answer:
a) x = v₀² sin 2θ / g
b) t_total = 2 v₀ sin θ / g
c) x = 16.7 m
Explanation:
This is a projectile launching exercise, let's use trigonometry to find the components of the initial velocity
sin θ = / vo
cos θ = v₀ₓ / vo
v_{oy} = v_{o} sin θ
v₀ₓ = v₀ cos θ
v_{oy} = 13.5 sin 32 = 7.15 m / s
v₀ₓ = 13.5 cos 32 = 11.45 m / s
a) In the x axis there is no acceleration so the velocity is constant
v₀ₓ = x / t
x = v₀ₓ t
the time the ball is in the air is twice the time to reach the maximum height, where the vertical speed is zero
v_{y} = v_{oy} - gt
0 = v₀ sin θ - gt
t = v_{o} sin θ / g
we substitute
x = v₀ cos θ (2 v_{o} sin θ / g)
x = v₀² /g 2 cos θ sin θ
x = v₀² sin 2θ / g
at the point where the receiver receives the ball is at the same height, so this coincides with the range of the projectile launch,
b) The acceleration to which the ball is subjected is equal in the rise and fall, therefore it takes the same time for both parties, let's find the rise time
at the highest point the vertical speed is zero
v_{y} = v_{oy} - gt
v_{y} = 0
t = v_{oy} / g
t = v₀ sin θ / g
as the time to get on and off is the same the total time or flight time is
t_total = 2 t
t_total = 2 v₀ sin θ / g
c) we calculate
x = 13.5 2 sin (2 32) / 9.8
x = 16.7 m
The center of mass of the two objects is the average position of the parts of the two object system
The center of mass of block <em>A</em>, and block <em>B</em> after displacement of block <em>B</em> is at <u>20 m from block </u><u><em>A</em></u>
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Reason:
The given parameters are;
The position of block A and block B at t = 0 is x = 0
The mass of block A, m₁ = 8 kg
Mass of block B, m₂ = 16 kg
Speed of block <em>A</em> = 0 m/s
Speed of block <em>B</em>, v₂ = 10 m/s
Location of the center of mass of the two object at t = 3 s; Required
Solution;
The location of block <em>A</em>, after 3 s is x₁ = 0 (block A is at rest)
The location of block <em>B</em>, = v₂ × t
The location of block <em>B</em>, after 3 s is x₂ = 10 m/s × 3 s = 30 m
The center of mass of two masses are given as follows;
The center of mass of the two objects is at at the position x = <u>20 m</u> (from block <em>A</em>)
Learn more about the center of mass here:
1) Mass of one copper atom:
2) There are atoms in the cube
3) Mass of the cubical block: 992 kg
Explanation:
1)
We are told here that the mass of one mole of copper is
for
(number of moles)
We also know that the number of atoms inside 1 mole of substance is equal to Avogadro number:
This means that atoms of copper have a mass of M = 64 g. Therefore, we can find the mass of one copper atom by dividing the total mass by the avogadro number:
2)
We are told that the diameter of a copper atom is
We can assume that the atoms are arranged in a cube, and that they are all attached to each other; so the side of the cube can be written as size of one atom multiplied by the number of atom per side:
where
N is the number of atoms (rows) in one side of the cube
Since the side of the cube is
L = 4.8 cm = 0.048 m
We find N:
This is the number of atom rows per side; therefore, the total number of atoms in the cube is
3)
The total mass of the cubical block of copper will be given by the mass of one atom of copper multiplied by the total number of atoms, so:
where:
is the number of atoms in the cube
is the mass of one atom
Therefore, substituting, we find:
So, the mass of the cubical block is 992 kg.
Learn more about mass and density:
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Answer:
6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
Explanation:
What matters is the part , the other parts of the equation don't affect time and space variations. We know that when the sign is - the wave propagates to the positive direction while when the sign is + the wave propagates to the negative direction, but <em>here is an explanation</em> of this:
For both cases, + and -, after a certain time (
), the displacement <em>y</em> of the wave will be determined by the
term. For simplicity, if we imagine we are looking at the origin (x=0), this will be simply
.
To know which side, right or left of the origin, would go through the origin after a time (and thus know the direction of propagation) we have to see how we can achieve that same displacement <em>y</em> not by a time variation but by a space variation
(we would be looking where in space is what we would have in the future in time). The term would be then
, which at the origin is
. This would mean that, when the original equation has
, we must have that
for
to be equal to
, and when the original equation has
, we must have that
for
to be equal to
<em>Note that their values don't matter, although they are a very small variation (we have to be careful since all this is inside a sin function), what matters is if they are positive or negative and as such what is possible or not .</em>
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In conclusion, when , the part of the wave on the positive side (
) is the one that will go through the origin, so the wave is going in the negative direction, and viceversa.