Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state → collision parameters → final state
v = 2 m/s 6 kg → v = 12 m/s 6 kg
tap an option below to select or change an answer (a + sign indicates a rightward direction; a - sign indicates a leftward direction)
δp = +14 kg·m/s f = +30 n, δt = 2 s f = +10 n, δt = 2 s impulse = +1.67 n·s impulse = + 10 n·s

Explanation:

Step1: Calculate initial momentum

$p_i = m\times v_i=6\times2 = 12\ kg\cdot m/s$

Step2: Calculate final momentum

$p_f = m\times v_f=6\times12 = 72\ kg\cdot m/s$

Step3: Calculate change in momentum

$\Delta p=p_f - p_i=72 - 12=60\ kg\cdot m/s$

Step4: Recall impulse - momentum theorem

Impulse $J=\Delta p$. Also, $J = F\times\Delta t$.

Step5: Check each option

For $F = + 30\ N,\Delta t=2\ s$, $J=F\times\Delta t=30\times2 = 60\ N\cdot s=60\ kg\cdot m/s$ (since $1\ N = 1\ kg\cdot m/s^{2}$)

Answer:

$F = +30\ N,\Delta t = 2\ s$