A 70.00 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player's speed afterward if the ball is thrown at (a) 15.0 m/s relative to the ground?

Video transcript

Hey, everyone in this problem, an ice skater with a mass of 60 kg is skating on a frozen lake at a constant velocity of 4m/s. The skater throws a 0.25 kg snowball straightforward with a velocity of 10 m per second. What is the skater's speed after throwing the snowball in a relative to the ground? We're given four answer choices. Option A 2.77 m per second. Option B 5.4, m/s. Option C3.9, m/s And option D 8.2, m/s. We're gonna draw a little diagram of what's going on in this problem. So we have an initial situation. Well, we have our ice skater pretend they have skates on and they're holding a snowball. Ok. Getting ready to throw it. Now, the initial velocity V knot Is four m/s. This is positive. We're gonna take to the right to be positive and that skater is gonna be moving towards the right. We know that the mass of the skater, MS is equal to 60 kg And the mass of the ball. OK? We're gonna say the mass of the Snowball MB is 0.2, five kg. All right, they're gonna throw that ball in front of them and we have a final situation where we have our ice skater, ok? And now the ball is somewhere in front of them. The mass of that snowball is still 0. kg. And the velocity final of that ball Is 10 m/s. The mass of our skater is still 60 kg and we wanna know what is their final velocity. So in this problem, we have no net external forces acting which tells us we have the conservation of momentum. OK? If we have conservation of momentum, then the initial momentum peanut is equal to the final momentum P F. What makes up these momentum? Well, we have two things in our system. We have our skater and we have our snowball. So we have to consider the initial momentum of this skater. OK, plus the initial momentum of the snowball. And same in the final case, we have the final momentum of the skater and the final momentum of the ball. What is momentum? While momentum is a mass multiplied by velocity? OK. So for each of these terms, we have mass multiplied by the corresponding velocity. We have MS multiplied by V SI plus M B multiplied by V B I is equal to M F oops MS sorry, multiplied by V S F plus M B multiplied by V B F. OK. So mass multiplied by velocity for each of these terms. OK. Now, we've used P knot and we've used P I both indicate initial. OK. So we wrote in general P and then we wrote P I um both of these indicate that initial time point. OK. All right. Now, I wanna substitute in the information we have, OK. We're looking for V S F And we know all of the other values. So we have the mass of this skater is 60 kg Multiplied by their velocity which is four m/s plus the mass of the snowball. 0.25 kg multiplied by their initial velocity. And well, the snowball is in that skater's arm, so they're moving together. So the speed of the snowball is the same as the speed of the skater. So that's gonna be four m per second And this is equal to 60 kg multiplied by V F S. So we've written it as BS F here, BS F plus the mass of the snowball, 0.2, five kg Multiplied by the final velocity of the Snowball, which is 10 m/s. Ok. We're gonna simplify now. So on the left-hand side and we have kilograms multiplied by meters per second. In each of these terms, we add them together and we get kg meters per second. This is equal to 60 kg multiplied by the velocity of the skater finally Plus 2.5 kgm/s. And we wanna isolate from VSF. So we can write that 60 kg multiplied by VSF Is equal to 238 0. kg m per second. OK. by subtracting that 2.5 to move it to the other side, we divide by 60 kg. K kilogram meters per second, divided by kilogram leaves us with a unit of meters per second, which is what we want for velocity. And we get that V S F is equal to 3.975 m per second. And so the final velocity of that skater is really, really close to their initial velocity of 4m/s, which makes sense because that snowball is so small compared to the skater that it shouldn't have a big impact. All right. So if we compare this to our answer choices, we see that the answer choices are rounded to three significant digits. And so if we round our answer, we found that the correct answer Is 3.98 m/s, which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.