Answer
We can rank them in order of magnitude of the momentum change, from smallest to largest:
$b \lt a = c = e \lt d \lt f$
Work Step by Step
(a) The magnitude of the velocity change is $20~m/s$
The magnitude of the change in momentum is $(6)(0.20~kg)(20~m/s) = 24~kg~m/s$
(b) The magnitude of the velocity change is $\sqrt{(10~m/s)^2+(10~m/s)^2} = 14.14~m/s$
The magnitude of the change in momentum is $(6)(0.20~kg)(14.14~m/s) = 17~kg~m/s$
(c) The magnitude of the velocity change is $20~m/s$
The magnitude of the change in momentum is $(6)(0.20~kg)(20~m/s) = 24~kg~m/s$
(d) The magnitude of the velocity change is $30~m/s$
The magnitude of the change in momentum is $(6)(0.40~kg)(30~m/s) = 72~kg~m/s$
(e) The magnitude of the velocity change is $10~m/s$
The magnitude of the change in momentum is $(6)(0.40~kg)(10~m/s) = 24~kg~m/s$
(f) The magnitude of the velocity change is $\sqrt{(10~m/s)^2+(30~m/s)^2} = 31.62~m/s$
The magnitude of the change in momentum is $(6)(0.40~kg)(31.62~m/s) = 76~kg~m/s$
We can rank them in order of magnitude of the momentum change, from smallest to largest:
$b \lt a = c = e \lt d \lt f$
