(d) Acceleration is a vector quantity
Answer:
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Explanation:
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Answer:
The arrow will leave the bow with a velocity of 10 m/s.
Explanation:
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The potential energy stored in the bow can be calculated using the following equation:
U = 1/2 · k · d²
Where
U = elastic potential energy.
k = spring constant.
d = stretched distance of the bow
Then:
U = 1/2 · 112 N/m · (0.29 m)²
U = 4.7 J
When the bow is released, the potential energy is transformed into kinetic energy. Then, the kinetic energy of the arrow when it leaves the bow will be:
KE = 1/2 · m · v² = 4.7J
Where:
KE = kinetic energy.
m = mass of the arrow.
v = velocity of the arrow:
Then:
4.7 J = 1/2 ·0.094 kg · v²
2 · 4.7 J / 0.094 kg = v²
9.4 kg · m²/s² / 0.094 kg = v²
v = 10 m/s
The arrow will leave the bow with a velocity of 10 m/s.
Explanation:
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Answer: 4.6 years
Explanation:
According to Kepler’s Third Law of Planetary motion <em>“The square of the orbital period 
of a planet is proportional to the cube of the semi-major axis 
(size) of its orbit”:
</em>
<em />
(1)
However, if is measured in Earth years, and is measured in astronomical units (unit equivalent to the distance between the Sun and the Earth), equation (1) becomes:
(2)
Knowing 
and isolating from (2):
(3)
(4)
Finally:
This is Ceres' orbital period
