A rocket of mass M is launched vertically fro | vedclass

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

Question

(C) By the law of conservation of energy,the total energy at the surface of the earth equals the total energy at the maximum height $h$.At the surface

Vedclass · Accepted Answer

$R / \left( \frac{2gR}{V^2} - 1 \right)$

Vedclass · Answer

(C) By the law of conservation of energy,the total energy at the surface of the earth equals the total energy at the maximum height $h$.At the surface: $E_i = K_i + U_i = \frac{1}{2}MV^2 - \frac{GM_eM}{R}$At maximum height $h$: $E_f = K_f + U_f = 0 - \frac{GM_eM}{R+h}$Equating $E_i = E_f$: $\frac{1}{2}MV^2 - \frac{GM_eM}{R} = - \frac{GM_eM}{R+h}$$\frac{1}{2}V^2 = GM_e \left( \frac{1}{R} - \frac{1}{R+h} \right)$Using $g = \frac{GM_e}{R^2}$,we have $GM_e = gR^2$.$\frac{V^2}{2} = gR^2 \left( \frac{R+h-R}{R(R+h)} \right) = \frac{gR^2h}{R(R+h)} = \frac{gRh}{R+h}$$\frac{V^2}{2gR} = \frac{h}{R+h}$$V^2(R+h) = 2gRh$$V^2R + V^2h = 2gRh$$V^2R = h(2gR - V^2)$$h = \frac{V^2R}{2gR - V^2}$Dividing numerator and denominator by $V^2$: $h = \frac{R}{\frac{2gR}{V^2} - 1}$

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

Similar Questions

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. The energy required to take this body from the surface of the earth to a height equal to twice the radius of the earth is:

Two masses $m_1$ and $m_2$ are at rest at infinity. Find their relative velocity of approach due to gravitational attraction when their separation is $d$.

$A$ rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance,the maximum height attained by the rocket above the surface of the earth is

What is the change in the gravitational potential energy of an object when it moves away from the Earth and when it comes closer to the Earth?

Vedclass Test Series

Exam Paper Generator

Online Exam Module