Aspace vehicle is traveling at 4150 km/h relative to the earth when the exhausted rocket motor (mass 4m) is disengaged and sent backward with a speed of 79 km/h relative to the command module (mass m). what is the speed of the command module relative to earth just after the separation? km/h

4213.2 Km/h

Explanation:

Given:

Initial Speed of space vehicle relative to Earth, u = 4150 km/h

Mass of rocket motor = 4m

speed of the rocket motor relative to command module , v'  = 79 Km/h

Mass of the command module = m

Now,

let the speed of command module relative to earth be 'v'

From the conservation of momentum, we have

( 4m + m ) × u = m × v + (4m × (v - v'))

or

5m × 4150 = mv + 4mv - 4mv'

or

20750 = 5v - ( 4 × 79 )

or

20750 = 5v - 316

or

v = 4213.2 Km/h

the closer the planet is to the sun, the larger the gravity

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)