Two astronauts, Michael and Collins, conduct several collision experiments in an environment with no external forces. Michael has a larger mass than Collins. In each experiment, Michael is initially moving with speed \(v_i\) in the positive \(x\)-direction and Collins is initially at rest.
In case A, Michael’s final velocity is \(0\text{.}\)
In case B, Michael’s final velocity is \(\frac{v_i}{4}\) in the negative \(x\)-direction.
In case C, Michael’s final velocity is \(\frac{v_i}{4}\) in the positive \(x\)-direction.
Rank the experiments by Collins’ final kinetic energy.
You throw a firecracker vertically upward. At \(t = 0\text{,}\) the firecracker is moving upward with speed \(v_1\text{,}\) at which point it begins to explode, splitting into an upper piece with mass \(m_u\) and a lower piece with mass \(m_l\text{.}\) The explosion finishes at \(t = \frac{v_1}{g}\text{,}\) at which point you observe that the upper piece is still moving upward with speed \(3v_1\text{.}\)
Determine the velocity of the lower piece at \(t = \frac{v_1}{g}\text{.}\)
