Here we're told that a neutron weighing 1.67 * 10 to the -27 kilograms is shot from a laser projector that is mounted 120 meters above the ground. Was its speed when it hits the ground. All right, so they're talking about the neutrons position initially, and then they're talking about shooting it towards the ground. Therefore it's converting into kinetic energy. From that information we should be able to calculate its speed or velocity.
Remember, kinetic energy can equal potential energy. Since they're both part of mechanical energy. That mean half times m * V2 = m * g * H Here the mask for both would be the same, since it's a neutron that's stationary first and then it's moving. We're looking for velocity or speed so that v2 is what we're solving for. Mass again is the same. Then we're going to say gravity duo. Acceleration here on Earth is 9.8 meters over second squared, and it's mounted 120 meters above the ground.
We're going to multiply these together and multiply everything here together. When we do that, we get 835 * 10 to the -28, and that's v2 = 1.96392 times 10 to the -24. Then we're going to divide both sides by 8.35 * 10 to the -28. So when we do that, that's going to isolate our v2 here. So when we do that, we're going to get v2 = 2 three 5-2, and that's going to be meters squared over, seconds squared.
Taking the square root of both of those sides will isolate our velocity or speed. So here when we do that, we get our velocity equal to four 8.4974 meters over seconds. Here, this has three sig figs. This has four sig figs. So let's just go with lease number sig figs. So that's going to be 48.5 meters per second. So that would be the speed or velocity of the neutron as it strikes the ground.