Two train whistles have identical frequencies of 1.85 102 Hz. When one train is at rest in the station and the other is moving n
1 answer:
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a) 2.64 s
We can solve this part of the problem by using the following SUVAT equation:
where
s is the displacement of the stone
u is the initial velocity
t is the time
a is the acceleration
We must be careful to the signs of s, u and a. Taking upward as positive direction, we have:
- s (displacement) negative, since it is downward: so s = -75.0 m
- u (initial velocity) positive, since it is upward: +15.5 m/s
- a (acceleration) negative, since it is downward: so a= g = -9.8 m/s^2 (acceleration of gravity)
Substituting into the equation,
Solving the equation, we have two solutions: t = -5.80 s and t = 2.84 s. Since the negative solution has no physical meaning, the stone reaches the bottom of the cliff 2.64 s later.
b) 10.4 m/s
The speed of the stone when it reaches the bottom of the cliff can be calculated by using the equation:
where again, we must be careful to the signs of the various quantities:
- u (initial velocity) positive, since it is upward: +15.5 m/s
- a (acceleration) negative, since it is downward: so a = g = -9.8 m/s^2
Substituting t = 2.64 s, we find the final velocity of the stone:
where the negative sign means that the velocity is downward: so the speed is 10.4 m/s.
c) 4.11 s
In this case, we can use again the equation:
where
s is the displacement of the package
u is the initial velocity
t is the time
a is the acceleration
We have:
s = -105 m (vertical displacement of the package, downward so negative)
u = +5.40 m/s (initial velocity of the package, which is the same as the helicopter, upward so positive)
a = g = -9.8 m/s^2
Substituting into the equation,
Which gives two solutions: t = -5.21 s and t = 4.11 s. Again, we discard the first solution since it is negative, so the package reaches the ground after
t = 4.11 seconds.
Answer:
The part that completes the nuclear equation is:
Explanation:
<h2>A) Preliminar explanation</h2>
The <em>nuclear equation</em> represents a nuclear reaction: the change of the nucleus of an atom.
The given equation represents an actinium atom releasing an alpha particle.
This is the meaning of each part of the equation:
- Ac is the chemical symbol of actinium
- The superscript to the left of the chemical symbol is the mass number of the atom (number of protons plus number of neutrons). The mass number is 225.
- The subscript to the left of the chemical symbol is the atomic number of the atom (number of protons). The atomic number is 89.
is the symbol of the alpha particle. It is an atom of helium
- The mass number is 4
- The atomic number is 2
To <em>complete the nuclear equation </em>you must do two balances: mass number balance and atomic number balance.
<u>i) Mass number balance</u>
- 225 = A + 4 ⇒ A = 225 - 4 = 221
<u>ii) Atomic number balance</u>
- 89 = Z + 2 ⇒ Z = 89 - 2 = 87
Therefore, the mass number of the unknown atom is 221, and the atomic number is 87.
From a periodic table, the element with atomic number 87 is francium, Fr.
Now, you have the chemical symbol, the atomic number, and the mass number of the unknown atom, which lets you to write the atom that completes the <em>nuclear equation</em>.