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2 years ago

explain why it is summer in the Southern hemisphere and winter in the northern hemisphere in December

Geography

1 answer:

DIA [1.3K]2 years ago

5 0

Answer:

Earth's tilted axis causes the seasons. Throughout the year, different parts of Earth receive the Sun's most direct rays. So, when the North Pole tilts toward the Sun, it's summer in the Northern Hemisphere. And when the South Pole tilts toward the Sun, it's winter in the Northern Hemisphere.

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4 years ago

A 215 kg rocket moving radially outward from Earth has a speed of 6.42 km/s when its engine shuts off 307 km above Earth's surfa

Vinvika [58]

<h2>GIVEN DATA</h2>

Mass of Rocket = m = 215 kg

Mass of Earth = M = $5.97*10^{24}$ kg

Radius of Earth = R = $6.37*10^6$ m

Gravitational Constant = G = $6.67*10^-11 \;\;m^3kg^{-1}s^{-2}$

Speed of Rocket = 6.42 km/s

Initial Height of Rocket from Earth's Surface = 307 km = $3.07*10^5$ m

Final Height of Rocket from Earth's Surface = 731 km = $7.31*10^5$ m

Initial Height from Earth's Centre = $R_i$ = $3.07*10^5 + 6.37*10^6 = 6.677*10^6$ m

Final Height from Earth's Surface = $R_f$ = $7.31*10^5 + 6.37*10^6 = 7.101*10^6$ m

(a) Kinetic Energy at Final Height = $K.E_f$

(b) Maximum Height of Rocket above Earth's Surface = $H_{max}$

<h2>EXPLANATION</h2>

Part (a):

As drag air is negligible, energy will be conserved.

$\therefore$ ΔE = 0

$K.E_i + U_i = K.E_f + U_f$

$K.E_f = U_f - K.E_i - U_i$

where, U is the potential energy of the system.

$K.E_f=\;G\frac{mM}{R_f} + \frac{1}{2}mv_i^2\;-\;G\frac{mM}{R_i}\;\;\;\;----------\;(1)$

Substituting Values and simplifying,

$K.E_f = 3.665*10^9 J$

Part (b):

The rocket will come to rest after reaching the maximum height. Therefore, its final velocity and consequently final kinetic energy will be zero.

$i.e.\;\;v_f = 0\;\;\;\&\;\;\; K.E_f=0$

Equation (1) will become,

$0\;=\;\;G\frac{mM}{R_f} + \frac{1}{2}mv_i^2\;-\;G\frac{mM}{R_i}$

$or\;\;\frac{1}{2}v_i^2= GM(\frac{1}{R_i}-\frac{1}{R_f})\\\\\frac{1}{2GM}v_i^2= (\frac{1}{R_i}-\frac{1}{R_f})\\\\\therefore\; R_f = \frac{2GMR_i}{2GM-v_i^2R_i}$

Substituting values and simplifying,

$R_f = 10.20*10^6 m$

which is the distance from the Earth's centre. To find the height of rocket from Earth's surface, we simply subtract the Earth's radius from above result.

$H_{max} = R_f - R$

$H_{max} = 10.20*10^6\;-\;6.37*10^6\\\\H_{max} = 3.83*10^6\;\;m$

4 0

3 years ago

explain why it is summer in the Southern hemisphere and winter in the northern hemisphere in December​

explain why it is summer in the Southern hemisphere and winter in the northern hemisphere in December