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dybincka [34]
3 years ago
13

A dwarf planet discovered out beyond the orbit of Pluto is known to have an orbital period of 619.36 years. What is its average

distance from the sun?
Physics
1 answer:
Maksim231197 [3]3 years ago
4 0

Answer: 72.66 AU=1.089(10)^{10} km

Explanation:

Let's begin by explaining that according to Kepler’s Third Law of Planetary motion “The square of the orbital period T of a planet is proportional to the cube of the semi-major axis a of its orbit”:

T^{2}\propto a^{3} (1)  

Now, if T is measured in years (Earth years), and a is measured in astronomical units (equivalent to the distance between the Sun and the Earth: 1AU=1.5(10)^{8}km), equation (1) becomes:  

T^{2}=a^{3} (2)  

So, knowing T=619.36 years and isolating a from (2) we have:  

a=\sqrt[3]{T^{2}} (3)  

a=\sqrt[3]{(619.36 years)^{2}} (4)  

Finally:

a=72.66 AU T his is the distance between the dwarf planet and the Sun in astronomical units

Converting this to kilometers, we have:

a=72.66 AU \frac{1.5(10)^{8}km}{1 AU}=1.089(10)^{10} km

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A baseball with a mass of 0.15 kilograms collides with a bat at a speed of 40 meters/second. The duration of the collision is 8.
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Explanation:

From the second law of motion given by Newton, Force is the rate change of momentum.

F = \frac{dp}{dt}=\frac {m dv}{dt} = \frac{m (v_f-v_i)}{dt}

Mass of the baseball, m = 0.15 kg

Initial velocity, v_i=-40 m/s (negative because direction of initial velocity is opposite to the final velocity)

Final velocity, v_f=50 m/s

The duration of collision, dt= 8.0 \times 10^{-3} s

Force, F = \frac{0.15 kg (50-(-40) m/s)}{8.0 \times 10^{-3} s}=1687.5 N

Hence, the value of force is 1687.5 N.

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A tennis player serves a tennis ball such that it is moving horizontally when it leaves the racquet. When the ball travels a hor
finlep [7]

Answer:

The initial velocity is 38.46 m/s.

Explanation:

The horizontal distance travel by the tennis ball = 13 m  

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Below is the calculation. Here, first convert centimetre into kilometre. So, height at which ball dropped is 0.56 km.

v = \sqrt{2 \times 9.8 \times 0.56} = 3.32 m/s \\

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Ux \times t = 13 \\

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Answer:

Because of the location, humidity and temperatures.

Explanation:

Coca is grown in humid and very humid subtropical forests, called yungas and

they form the lower floor of the upper Jungle, in the Central Andes, mostly in Peru and Bolivia. The  yungas are in contact with the rainforests of the lowlands in Amazonia, where it has been  started to expand coca cultivation recently (Dourojeanni, 1988). The optimum altitude is 1000 a  2000 meters (where cocaine content is higher), with optimal annual average precipitation, is 2000 meters  mm, but it is grown between 700 and 2000 msnm and with an average annual rainfall of 1000 to 4200 mm.

msnm = meters above sea level

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