a nasa explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary…

a nasa explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary asteroid. if the velocity of the spacecraft is 250 m/s and the asteroid is pushed back -25 m/s, what is the mass of the asteroid? assume there is no net force on the system.\n\n100 kg\n6,250 kg\n10,000 kg\n6,250,000 kg

a nasa explorer spacecraft with a mass of 1,000 kg takes off in a positive direction from a stationary asteroid. if the velocity of the spacecraft is 250 m/s and the asteroid is pushed back -25 m/s, what is the mass of the asteroid? assume there is no net force on the system.\n\n100 kg\n6,250 kg\n10,000 kg\n6,250,000 kg

Answer

Explanation:

Step1: Apply conservation of momentum

$m_1v_1 + m_2v_2=0$ (initial momentum is 0 as system is stationary). Let $m_1 = 1000$ kg be mass of spacecraft, $v_1 = 250$ m/s be its velocity, $m_2$ be mass of asteroid and $v_2=- 25$ m/s be asteroid's velocity.

Step2: Rearrange for mass of asteroid

$m_2=-\frac{m_1v_1}{v_2}$ Substitute values: $m_2 =-\frac{1000\times250}{-25}$ $m_2 = 10000$ kg

Answer:

10,000 kg