Momentum: Ice skater throws a ball

welcome back I'll now do a couple of more momentum problems so this first problem I have this ice skater and she's on an ice skating rink and what she's doing is she's holding a ball and this ball let me draw the ball this is a point one five kilogram ball two point one five kilogram ball and she throws it she throws it let's just say she throws it directly straight forward in front of her although she's staring at us she's actually forward for her body so she throws it exactly straight for it I don't understand it it's hard to throw something straight forward but let's assume that she can so she throws it exactly straight forward with a speed or since we're going to give the direction as well it's a velocity right because speed is just the magnitude while velocity is a magnitude and a direction so she throws the ball at thirty five meters per second and this ball is 0.15 kilograms you know what the problem says is that their combined mass their combined mass her plus the ball is 50 kilograms 50 kilograms and the question is after she throws the ball so they're both stationary before she does anything and then she throws this ball and the question is after throwing this ball what is her recoil velocity or essentially how much by throwing the ball did does she push herself backwards so what is her velocity in the backward direction and if you're not familiar with the term recoil recoil it's often applied to when someone I guess you know not that we want to think about violent things but if you shoot a gun your shoulder recoils back because once again momentum is conserved so there's a certain amount of momentum going into that bullet which is very light and fast going forward but since momentum is conserved your shoulder has has velocity backwards but if we will do another problem with that let's get back to this problem so like I just said momentum is conserved so what's the momentum at the start of the problem so the initial momentum well let's say let's make let's let me do different colors so this is the initial momentum initially the mass is 50 kilograms right concerning the ball combined or 50 kilograms times the velocity well the velocity is zero so initially there is zero velocity in the system zero velocity so the momentum is zero P equals let's say P initial is equal to zero and since we start with a net zero momentum we have to finish with a net zero momentum so what's momentum later well we have a ball moving at 35 meters per seconds and the ball has a mass of 0.15 kilograms so it's point one five kilograms I'll ignore the unit's for now just to save space times the velocity of the ball times 35 meters per second so this is the momentum of the ball plus the new momentum of the figure skater so what's her her mass well her mass is going to be 50 minus this actually won't matter a ton but let's say it's 49 49 point what is that point 85 kilograms times her new velocity times velocity let's call that the velocity of the skater and so let me get my trusty calculator out okay so let's see point one five times 35 so let's see point one five times 35 is equal to five point two five so that equals five point two five plus forty nine point eight five times the skaters velocity the final velocity and of course this equals zero because the initial velocity was zero so let's let's subtract point five point two five from both sides and then the equation becomes minus five point two five is equal to forty nine point eight five times the velocity of the skater so we're essentially saying that the momentum of just the just the ball is five point two five and since we have a combined system has to have zero net momentum we're saying that the momentum of the skater has to be 5.25 in the other direction going backwards or has a momentum of minus five point two five and to figure out the velocity we just divide her momentum by her mass and so divide both sides by forty-nine point eight five and you get the velocity of the skater so let's say let's make this a negative number divided by forty nine point eight five equals minus point 105 so minus point minus isn't too low ignorin minus point one zero five meters per second so that's interesting when she throws this ball out at 35 meters per second which is pretty fast she will recoil back at about about 10 centimeters about yeah roughly 10 centimeters per second so she will recoil a lot slower although she will move back and if you think about it this is this is a form of propulsion this is how Rockets work they eject something that maybe has less mass but super fast and that since we have a conservation of momentum it it makes the rocket move in the other direction well anyway let's see if we could do fit another problem in this actually it's probably better to leave this problem done and then I aha more time for the next problem which will be slightly more difficult see you soon