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

For an object projected from the Earth,on which two factors does the escape velocity $NOT$ depend?

What is the escape velocity for the surface of a black hole?

$A$ planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 \ km/s$,the escape velocity from the surface of the planet would be ........ $km/s$.

$A$ body is projected vertically upward from the surface of the earth of radius $R$ into space with velocity $n V_e$ (where $n < 1$ and $V_e$ is the escape velocity). The maximum height from the surface of the earth to which the body can reach is

$A$ spaceship moves from the Earth to the Moon and back. The greatest energy required for the spaceship is to overcome the difficulty in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module