Chapter 10.4, Problem 7STP

The radius of Earth is about 6378 kilometers. The escape velocity $V_e$ is determined by the function $V_e=\sqrt{2gR}$

where g is acceleration due to gravity in m/s² and R is the radius of Earth in meters, if g for Earth is 9.8 m/s², what is the escape velocity of Earth? Show your work.

To determine

To find: the escape velocity of earth.

Answer to Problem 7STP

The escape velocity of earth is $3535.65m/s$ .

Explanation of Solution

Given information:

The function is $V_e=\sqrt{2gR}$ .

Calculation: to find the solution, first substitute and then simplify,

  $\begin{array}{l}{V}_e=\sqrt{2gR}\\ V_e=\sqrt{2\left(9.8\right)\left(6378\right)\left(100\right)}\text{ [substitute]}\\ V_e=\sqrt{12500880}\text{ [multiply]}\\ V_e=3535.65\text{ [square root]}\end{array}$

Thus, The escape velocity of earth is $3535.65m/s$ .