A baseball with a mass of 503 g possesses a kinetic energy of 0.815 kJ. Calculate its velocity in m/s.

Here we're told that a baseball with a mass of 503 grams possesses a kinetic energy of 0.815 kilojoules. Calculate its velocity in meters per second. So in this question they're giving us the mass, they're talking about kinetic energy, and they're asking us to determine the velocity. Because we're dealing with mass and velocity, that means kinetic energy equals half times mass times velocity squared. In terms of kinetic energy, we want the units to be in joules. So we're gonna say here for every 1 kilojoule it's 10 to the 3 joules. And the reason we want it in joules is because remember joules also equals kilograms times meter squared over seconds squared. Having these units, we'll see how things cancel out so that we'll have meters per second at the end for our velocity. So we're gonna say here we have 815 kilograms times meter squared over second squared equals half times my mass needs to be in kilograms. So grams go on the bottom, kilograms go on top. 1 kilo is 10 to the 3. So this is 0.503 kilograms. And then we have v squared that we're trying to isolate. So here when we work this out, we're going to multiply both sides by 2, and that's gonna give me 1630 kilograms times meter squared over second squared. And then we're gonna say we actually have enough space, so we're gonna say we have equal to 0.503 kilograms times velocity squared. Divide both sides now by 0.503, kilograms. So when we do that we'll see that that kilograms cancel out. So we'll bring it over here, v squared equals, after we divided by 0.503, we're gonna have 3240.5666, 5.5666 6 meters squared over seconds squared. Take the square root of both sides and that'll give us just velocity The meter squared and the second squared had got square rooted as The meter squared and the second squared have got square root as well, so that's why it drops down to just meters over seconds. So we can see that by converting kilojoules to joules, and then realizing that joules equals kilograms times meters squared over seconds squared, we're able to find our final units for velocity in meters per second.