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3 years ago

The primary export of the Arabian Peninsula is gold. true or false

2 answers:

5 0

Answer: FALSE.

Explanation:
The primary export of the Arabian Peninsula is oil. Saudi Arabia is the world´s larger exporter of oil

3241004551 [841]3 years ago

3 0

FALSE the primary export of the Arabian Peninsula is not gold

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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.

$H_{max} = R_f - R$