A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the glider's velocity just after the skydiver lets go?

Video transcript

Hey everyone in this problem, we have a humanitarian helicopter of total mass 11,500 kg, including the pilots and the food boxes that releases vertically. A 150 kg box of food. The helicopter is flying at a constant speed of 45 m per second in the X direction. And we're asked to find the boxes speed immediately after it was released. Ok. We're given four answer choices. Option A 0 m per second. Option B negative 45 m per second I hat, option C 45 m per second I hat and option D is that we can't determine this from the given information. Now, when we think about this, conceptually, we have this helicopter flying at 45 m per second in the X direction and this box is gonna be dropped vertically. Ok? So that initial speed of the box relative to the helicopter is just going to be zero. Ok. It's not being given any extra X speed. And so we would expect that its initial speed is going to be the exact same as the helicopter in the X direction. Now, how can we show this mathematically? Well, remember, recall the conservation of momentum we have the, the initial momentum is equal to the final moment. Now, what's our initial momentum? Well, that's just gonna be a pea, no. Ok. And that's gonna be that momentum of the entire helicopter pilot food box system. Ok. And the final momentum is gonna be made up of these two things split up. We're gonna have the final momentum of the box PFB plus the final momentum of the helicopter. PFH. And when I say helicopter, I mean, helicopter and pilots now recall that momentum is equal to the mass multiplied by the velocity. And so on the left hand side, we have the total mass mt multiplied by the initial speed V knot. This is equal to MB, the mass of the food box multiplied by VFB that speed of the food box immediately after it's released, which is what we're looking for. Pull us the mass of the helicopter mh multiplied by the velocity of the helicopter after that box is released. Now, our total mass, we're told that that's 11,500 kg. So we can substitute that in and that's multiplied by that initial speed. Now, we're told the helicopter is flying at a constant speed of 45 m per second. And so this is going to be equal to 45 m per second. On the right hand side, we have the mass of the food box 150 kg multiplied by its velocity after being released, that value we're looking for plus the mass of the helicopter. Ok? No, initially, the helicopter was 11,500 kg. But now we've dropped this 150 kg box of food out of it. And so the mass of the helicopter, ok? And the pilots and everything else in it is actually going to be 11,500 kg minus that 150 kg that was dropped out of it. And the speed of the helicopter is the same. It's still flying at a constant speed. And so we have 45 m per second there. Now we can rearrange this. So we have 150 kg multiplied by that final speed of that food box that we're looking for. And this is going to be equal to, we're gonna factor out the speed of 45 m per second. We're gonna move the entire second term on the right hand side to the left by subtracting it. Ok. So when we factor 45 m per second, we have 11,500 kg, ok? That comes from the left hand side and then we're gonna subtract this entire mask from the right hand side. 11,500 kg minus 150 kg. So on the left, we still have 150 kg multiplied by that speed of the food box or the velocity of the food box. I should say on the right hand side, we have 45 m per second. In the brackets, we have 11,500 kg minus 11,500 kg. That gives us zero and then we have minus negative 100 and 50 kg which gives us positive 100 and 50 kg. So all of that simplifies to 100 and 50 kg. Now we have 100 and 50 kg. On both sides, we can divide by 100 and 50 kg. When we get that, the speed of the box is equal to 45 m per second. Ok. Exactly what we expected when we talk this out, conceptually, it's going to be moving at the exact same speed in the X direction as the helicopter. And so the correct answer here is going to be C 45 m per second in the I hat direction. Thanks everyone for watching. I hope this video helped see you in the next one.