Question

A particle is fired vertically upward with a speed of 15 km/s.With what speed will it move in interstellar space.Assume only earth gravitational field.

Answer 1

Take root both side... That would be the answer

:)

Answer 2

Dear Student,

◆ Answer -

Speed of particle in interstellar space = 10.1 km/s.

● Explanation -

Let v be initial speed and v' be speed in interstellar space.

Kinetic energy will be used up for work done in escaping earth's gravitation.

KE = W

1/2 mv^2 - 1/2 mv'^2 = ʃ(GMm/x^2).dx

1/2 m(v^2 - v'^2) = GMm/R

1/2 (v^2 - v'^2) = GM/R

Substitute values,

1/2 [(15×10^3)^2 - v'^2] = 6.67×10^-11 × 6×10^24 / 6.4×10^6

Solving this,

v' = 1.01×10^4 m/s

v' = 10.1 km/s.

Hence, speed of particle in interstellar space is 10.1 km/s.

Thanks dear. Hope this helps you...