00:02
Okay, so we have this 45 -kilogram girl walking along a plank.
00:07
Initially, they both start at rest.
00:09
The plank has a mass of 150 kilograms, and she is walking with respect to the plank with a speed of 1 .50 meters per second.
00:18
Now, to find her speed with respect to the ice, we first need to figure out the relationship between her speed and the plank's speed.
00:30
So for that, we can use the conservation of momentum.
00:33
Where initially their momentum was zero, and then they're both going to have some momentum, some momentum of the girl and the momentum of the plank with respect to the ice.
00:43
So plugging in our equation for momentum and then solving for the speed of the plank with respect to the ice, we get this relationship here, where the speed of the plank with respect to ice is equal to the negative value of the ratio of their masses times the speed of the group, girl with respect to the ice.
01:06
Now we can use that and we can plug it into this relationship here, where the girl's speed with respect to the ice is going to be equal to her speed with respect to the plank plus the plank's speed with respect to the ice.
01:23
So we're going to take this value, we're going to plug it in for that speed of the plank.
01:28
So we're going to get here.
01:30
And since this is negative and we have the speed of the girl with respect to the ice on both sides...