Question

(a) A space vehicle is launched vertically upward from the Earth's surface with an initial speed of vi that is comparable to but less than the escape speed vesc . What maximum height does it attain?

Answer 1

Energy Conservation Theory,

$(k+v)_i=(k+v)_f \quad \text { (No air resistone)}$

$\frac{1}{2} m v_i^2-\frac{G m M_\epsilon}{R_\epsilon}=0-\frac{G m M_\epsilon}{R_\epsilon+h}$

$\frac{1}{2} m v_i^2-\frac{G m M_\epsilon}{R_\epsilon}=0-\frac{G m M_\epsilon}{R_\epsilon+h}$

$v_{e x^2}{ }^2-v_i^2=\frac{v_{e^2 R_t} R_t}{R_t t h}\\&\frac{1}{v_{B C^2-v_1^2}^2}=\frac{R_E+h}{v_{e^2 R_E} R_E}\\\\\\h=\frac{R_E V_1^2}{v_{\text {esc }}^2-v_1^{\beta^2}}$

What is law of  energy conservation?

The principle of energy conservation states that energy is neither created nor destroyed.  It may change from one sort to another. Just like the mass conservation rule, the legitimacy of the preservation of energy depends on experimental perceptions; hence, it is an experimental law. The law of preservation of energy, too known as the primary law of thermodynamics

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