A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio v(son)/v(mother) of their speeds?

Video transcript

Hey, everyone. So this problem is working with kinetic energy. Let's see what they're asking us. So we have a proton of a given mass and a dude Iran of another given mass. And we're told that they have the same amount of kinetic energy. We're asked to find the speed of the proton in terms of the speed of the dude Iran. So what that's gonna look like you can see in our answers, it's the V sub P equals some constant times V sub deep. So the first thing we can do is recall that our kinetic energy is given by K equals one half M V squared. So we already know from the problem that the kinetic energies are the same. So K P equals K D and we're also given the masses. So M P an M D or given to us, and we can actually create a ratio between those two and then set the kinetic energy is equal to each other to solve for the speeds. So if we take are the mass of the neutron M D divided by M P, we get two, which makes sense just based on what we know about particles. A dude Iran is twice the mass of a proton because it has one proton and one nuclear one neutron. So we're gonna make it out of that here. So two MP M D and then we'll rewrite this equation in terms of both the proton and the neutron. So one half M P B P squared equals one half M D V D squared R has canceled. And we know that MD is actually a two MP. So we're gonna sub that in and the mps cancel. So we're asked to solve for V P in terms of V D. So the only thing we have left to do is take the square root of both sides and we get V P equals the square root of two V D squared, Which simplifies just where we have two times VD. And so when we look at our potential answers that aligns with choice A and so A is the correct answer for this problem. That's all for this one, we'll see you in the next video.