Question

A space ship that is out of fuel is traveling through space with
a speed 10 m/s. The **total mass** of the space ship
and its empty fuel tank is 900 kg. What is the momentum of the
space ship (with the empty fuel tank attached)? What is the total
kinetic energy of the space ship (with the empty fuel tank
attached)? Since there is no more fuel, the 200 kg fuel tank is
disconnected and released in the opposite direction at 4 m/s. At
what speed is the rest of the space ship now traveling? What is the
total kinetic energy of the system after the fuel tank is
disconnected? Was this process (the fuel tank being released)
elastic or inelastic?

Answer #1

What is the momentum of the space ship (with the empty fuel tank attached)

p = mv

p = 900 * 10

p = 9000 Kg.m/s

_________________

What is the total kinetic energy of the space ship (with the empty fuel tank attached)

K.E = 1/2 * m * v^{2}

K.E = 1/2 * 900 * 10^{2}

K.E = 45000 J

____________________

At what speed is the rest of the space ship now traveling

suppose initially spaceship ( with tank) was moving in + direction, then

using conservation of momentum

mv = m (tank) * v ( tank) + m ( spaceship) * v ( spaceship)

9000 = 200 * -4 + 700 * v ( spaceship)

so,

v ( spaceship) = 14 m/s ( in initial direction of motion

________________________

What is the total kinetic energy of the system after the fuel tank is disconnected

1/2 * 700 * 14^{2}

K.E = 68600 J

_______________________

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