Suppose the gravitational force of the Earth on a body was
) What escape velocity v_e would a body need to escape the gravitational field of the Earth?

Question

Suppose the gravitational force of the Earth on a body was )What escape velocity v_e would a body need to escape the gravitational field of the Earth?

Quizplus · Accepted Answer

Escape velocity is given by v = sqrt(2GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the Earth's center and the object. Plugging in the given gravitational force, we can solve for r using F = GMm/r^2, where m is the mass of the object. This gives r = sqrt(GM/F), which is approximately 6.38 x 10^6 m (the radius of the Earth). Plugging this into the escape velocity formula, along with the values for G and M, gives v = sqrt(2*(6.67 x 10^-11)*(5.97 x 10^24)/(6.38 x 10^6)), which is approximately 11.2 km/s. The closest choice is B, which matches this value.

Suppose the Gravitational Force of the Earth on a Body