Answer:
Explanation:
M = Mass of Earth = 5.972 × 10²⁴ kg
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
r = Radius of Earth = 6371000 m
[tex]v_i[/tex] = Launch velocity = 14.8 km/s
[tex]v_f[/tex] = Final velocity
r = Orbit distance = [tex]3.84\times 10^8\ m[/tex]
m = Mass of satellite
As the energy of the system is conserved we have
[tex]U_i+K_i=U_f+K_f\\\Rightarrow -\dfrac{GMm}{r}+\dfrac{1}{2}mv_i^2=-\dfrac{GMm}{R}+\dfrac{1}{2}mv_f^2\\\Rightarrow -\dfrac{GM}{r}+\dfrac{1}{2}v_i^2=-\dfrac{GM}{R}+\dfrac{1}{2}v_f^2\\\Rightarrow \dfrac{1}{2}v_f^2=\dfrac{GM}{R}-\dfrac{GM}{r}+\dfrac{1}{2}v_i^2\\\Rightarrow v_f=\sqrt{2GM(\dfrac{1}{R}-\dfrac{1}{r})+v_i^2}\\\Rightarrow v_f=\sqrt{2\times 6.67\times 10^{-11}\times 5.972\times 10^{24}\times (\dfrac{1}{6.371\times 10^6}-\dfrac{1}{3.84\times 10^8})+14800^2}\\\Rightarrow v_f=18493.53507\ m/s[/tex]
The meteroid's speed as it hits the earth is 18493.53507 m/s
