Question

a satellite orbiting earth at a velocity of 3700 m/s collides with a piece of space debris traveling at 5000 m/s. if the objects have the same mass and the space debris has a velocity after collision of 3700 m/s, what is the velocity of the satellite after the collision?

a. 6200 m/s
b. 7800 m/s
c. 3700 m/s
d. 5000 m/s

Explanation:

Step1: Apply conservation of momentum formula

$m_1u_1 + m_2u_2=m_1v_1 + m_2v_2$. Since $m_1 = m_2=m$, the formula becomes $mu_1+mu_2 = mv_1+mv_2$, and can be simplified to $u_1 + u_2=v_1 + v_2$.

Step2: Substitute given values

Let $u_1 = 3700$ m/s (satellite initial velocity), $u_2 = 5000$ m/s (debris initial velocity), $v_2 = 3700$ m/s (debris final velocity). Substitute into $u_1 + u_2=v_1 + v_2$: $3700+5000=v_1 + 3700$.

Step3: Solve for $v_1$

$v_1=3700 + 5000-3700=5000$ m/s.

Answer:

D. 5000 m/s