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.\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.\n100 kg\n6,250 kg\n10,000 kg\n6,250,000 kg

Answer

Explanation:

Step1: Apply law of conservation of momentum

Since there is no net force, initial momentum $P_i = 0$ (system is initially stationary). Final momentum $P_f=m_1v_1 + m_2v_2$, where $m_1$ is mass of spacecraft, $v_1$ is its velocity, $m_2$ is mass of asteroid and $v_2$ is its velocity. And $P_i = P_f$, so $0=m_1v_1 + m_2v_2$.

Step2: Rearrange formula to solve for $m_2$

We get $m_2=-\frac{m_1v_1}{v_2}$. Given $m_1 = 1000$ kg, $v_1=250$ m/s and $v_2=- 25$ m/s.

Step3: Substitute values

$m_2=-\frac{1000\times250}{-25}=\frac{250000}{25}=10000$ kg.

Answer:

10,000 kg