Question

pre - and post - collision information is shown. identify the collision parameters that are consistent with the indicated change in momentum.
initial state
p = 9 kg*m/s
3 kg
collision parameters
f = +3 n, δt = 9 s
final state
p = 27 kg*m/s
3 kg
tap an option below to select or change an answer. (a + sign indicates a rightward direction; a - sign indicates a leftward direction.)
f = +3 n, δt = 9 s
f = +12 n, δt = 3 s
f = +9 n, δt = 2 s
f = +36 n, δt = 3 s
f = +18 n, δt = 6 s

Explanation:

Step1: Recall impulse - momentum theorem

The impulse - momentum theorem states that $J=\Delta p$, where $J = F\Delta t$ and $\Delta p=p_f - p_i$.

Step2: Calculate the change in momentum

Given $p_i = 9\ kg\cdot m/s$ and $p_f=27\ kg\cdot m/s$, then $\Delta p=p_f - p_i=27 - 9=18\ kg\cdot m/s$.

Step3: Check each option for impulse

For option 1: $F = 3\ N,\Delta t = 9\ s$, $J_1=F\Delta t=3\times9 = 27\ N\cdot s$.
For option 2: $F = 12\ N,\Delta t = 3\ s$, $J_2=F\Delta t=12\times3=36\ N\cdot s$.
For option 3: $F = 9\ N,\Delta t = 2\ s$, $J_3=F\Delta t=9\times2 = 18\ N\cdot s$.
For option 4: $F = 36\ N,\Delta t = 3\ s$, $J_4=F\Delta t=36\times3=108\ N\cdot s$.
For option 5: $F = 18\ N,\Delta t = 6\ s$, $J_5=F\Delta t=18\times6 = 108\ N\cdot s$.

Answer:

$F = +9\ N,\Delta t = 2\ s$