A rocket is flying at a constant speed of 300 metres per second while rising vertically. The rocket’s engines provide a force of 5000 newtons and the drag from the air around the rocket produces a 3000-newton force. What is the weight of the rocket?
Now, this is one of those really sneaky rude evil questions. And the people who wrote it are probably sitting in the seat laughing like a super villain because they’ve come up with something so diabolical. So we need to be really, really careful here. Let’s start by underlining the important information given to us in the question.
So we’ve got a rocket flying at a constant speed of 300 metres per second whilst rising vertically. That’s important. We know that the rocket’s engines provide a force of 5000 newtons and the drag from the air due to air resistance is 3000 newtons. What we’re asked to do is to find the weight of the rocket. So what we should do first is to draw a diagram and label all the forces acting on the rocket. It’s also important that we’ve drawn the rocket to be rising vertically. That’s specified in the question.
So let’s label the first force, which is 5000 newtons generated by the engines of the rocket. Obviously, the rocket’s engines are gonna work in the direction of the rocket. So it’s gonna propel the rocket in this case upwards. And that’s why we’ve drawn the force from the engines pointing upwards.
The other force that we’ve been given in the question is the drag. That happens to be 3000 newtons. And it will be working against the rocket’s direction of motion. This is because air resistance or more generally drag works against motion. So it’s gonna try and slow the rocket down. And we can kind of see why if we imagine air to be these orange sheets of fluid.
As the rocket blasts upwards, it exerts a force on the sheets of air, which means that they will exert an opposing force back on the rocket. So they’re gonna try and resist the motion. This by the way is Newton’s third law of motion: every action has an equal and opposite reaction. As the rocket travels upwards and exerts an upwards force on the air, the air exerts a downwards force back on the rocket.
Anyway, let’s see if we’ve got any other forces to think about on the rocket. Well, yes, we do. In fact, the third force on the rocket is mentioned in the question. It’s the weight of the rocket and that’s what we’re trying to find. Obviously, weight will act in a downward direction because it acts towards the center of the Earth. And in this case, because the rocket is travelling upwards is gonna act against the direction of the motion.
So how we’re gonna go about finding the weight of the rocket? Well, we’ve already seen Newton’s third law of motion. But right now, we need to use another one of his laws. We need to use Newton’s first law of motion. Newton’s first law states that an object at rest stays at rest and an object travelling at a constant speed continues to travel at that speed unless acted on by an unbalanced force. So let’s break that down.
What Newton’s first law is basically trying to tell us is that if there are no unbalanced forces acting on an object, then if it was already stationary — if it was already at rest — then it continues to be at rest. And similarly if the object was already travelling at a constant speed, as long as there are no unbalanced forces on it, it will continue to travel at that constant speed.
So what does an unbalanced force mean? Well, we know that when we have a group of forces acting on an object, we have to add them as vectors. An unbalanced force just means that when you add up all the forces vectorially, there is a net force or in other words the overall force on an object is not zero. That’s when the forces unbalanced. When the forces on an object cancel each other out, the overall net force is zero and it’s said to be balanced.
So in order for an object to continue to travel at a constant speed that it was travelling at before, the forces on the object must be balanced. Now, our rocket is travelling at a constant speed of 300 metres per second. But regardless of what that speed is, the forces on the rocket must be balanced because otherwise it would either accelerate or decelerate. But that’s not happening. It’s travelling at a constant speed. So the forces are balanced. Now, the only forces acting are either in an upward direction or a downward direction. So that makes life a little bit easier for us.
In order for the net force on the rocket to be zero, which is what we require because the rocket is travelling at a constant speed, the upwards forces must exactly cancel out the downwards forces or in other words, the magnitude or size of upward forces must be equal to the magnitude or size of downward forces. That way, the reason they cancel each other out is because they act in opposite directions.
So the magnitude of upwards forces, well, in this case, there’s only one force, which is the 5000 newtons. This must be equal to the magnitude of downward forces, which is the 3000 newtons from the drag, plus the weight of the rocket 𝑤. Subtracting 3000 from both sides of the equation gives us 2000 is equal to 𝑤 or the weight of the rocket is equal to 2000 newtons.
So at the beginning of the video, I said that this question was sneaky, wiley, and rude. Why did I say that? Well, that’s because it’s one of those trick questions — one of those red herring questions — because it gives us the value of 300 metres per second as the constant speed of the rocket. That value was irrelevant to our calculation. We did not need to know how fast the rocket was travelling.
The only thing that’s relevant in this case is the fact that the rocket is travelling at a constant speed. It doesn’t matter what that speed actually is. We can have exactly the same answer for the weight of the rocket with exactly the same forces acting on it even if the rocket was travelling at three metres per second.
And this is something you need to be aware of: sometimes there’ll be some red herrings in questions because they’re there to test your understanding of the subject. So think through the question thoroughly, underline all the important bits, and see if it makes sense to not include something that’s been given in the question in your calculations.