A rocket is launched straight up from the sur | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given,escape velocity on the surface of the earth is $v_e = \sqrt{\frac{2GM_e}{R_e}} = 11.2 \ km/s$. At an altitude $h = \frac{R_e}{3}$,the distan

Vedclass · Accepted Answer

$9.7$

Vedclass · Answer

(C) Given,escape velocity on the surface of the earth is $v_e = \sqrt{\frac{2GM_e}{R_e}} = 11.2 \ km/s$. At an altitude $h = \frac{R_e}{3}$,the distance from the center of the earth is $r = R_e + h = R_e + \frac{R_e}{3} = \frac{4R_e}{3}$. To escape from this point,the kinetic energy of the rocket must be equal to the magnitude of the gravitational potential energy at that distance. $\frac{1}{2}mv_{e1}^2 = \frac{GM_em}{r} = \frac{GM_em}{4R_e/3} = \frac{3GM_em}{4R_e}$. Since $v_e^2 = \frac{2GM_e}{R_e}$,we have $\frac{GM_e}{R_e} = \frac{v_e^2}{2}$. Substituting this into the energy equation: $\frac{1}{2}v_{e1}^2 = \frac{3}{4} \left(\frac{v_e^2}{2}ight) = \frac{3}{8}v_e^2$. $v_{e1}^2 = \frac{3}{4}v_e^2 \Rightarrow v_{e1} = \frac{\sqrt{3}}{2}v_e$. Given $v_e = 11.2 \ km/s$,$v_{e1} = \frac{1.732}{2} 	imes 11.2 = 0.866 	imes 11.2 \approx 9.7 \ km/s$.

Similar Questions

The escape velocity from the moon's surface is less than that on the earth's surface,because:

An object is thrown directly away from the surface of the earth with an initial speed $v$. The object reaches up to a height of $\frac{4}{5} R_E$ from the earth's surface,where $R_E$ is the radius of the earth. If the escape velocity of the object is $v_E$,then the value of $\frac{v}{v_E}$ is:

The radius of the planet is double that of the earth,but their average densities are same. $V_{p}$ and $V_E$ are the escape velocities of planet and earth respectively. If $\frac{V_p}{V_E}=x$,the value of '$x$' is

Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ($R$ - Radius of the earth).

Vedclass Test Series

Exam Paper Generator

Online Exam Module