A 5.5-kg object moving in the +𝓍 direction at 6.5 m/s collide...

Question

A 5.5-kg object moving in the +𝓍 direction at 6.5 m/s collides head-on with an 8.0-kg object moving in the ―𝓍 direction at 4.0 m/s. Determine the final velocity of each object if the 5.5-kg object is at rest after the collision.

Accepted Answer

Hey, everyone in this problem, we're told that before they collide a sailboat that has a mass of 6.1 kg is traveling to the right at a speed of 5.6 m per second. Meanwhile, a remote controlled boat with a mass of 8.1 kg is moving to the left towards the sailboat at a speed of 4.1 m per second. And so we're gonna stop there. We're gonna come back to the rest of this question in just a minute. But first, we're gonna draw what we have going on before this collision. Ok. So before the collision, we have a sailboat, we're just gonna draw it as a circle. Hm. And we're told that the mass of this sailboat which we'll call MS is 6.1 kg and the sailboat is traveling to the right at a speed of 5.6 m per second. Now, we're gonna take the right word direction to be our positive direction. That means that we're gonna have a positive velocity here. So the initial velocity of the sailboat V not S is going to be 5.6 m per second. Then we also have a remote controlled boat and it has a massive 8.1 kg. So it's a little bit bigger and we're gonna use subscript B. So the mass of the boat MB is 8.1 kg and it is moving to the left towards the sailboat. It has a speed of 4.1 m per second because it's moving to the left in our negative direction, that's gonna be a negative velocity. So the initial velocity of the boat V not B is going to be negative 4.1 m per second. So that's everything we've been told so far. Let's go back to the question and see what we're asked to do. We're told that after they collide the sailboat stops moving and we're asked to determine the speed and direction of the remote controlled boat after the collision. We're given four answer choices. Option A 0.12 m per second in the positive extraction. Option B 1.2 m per second in the negative X direction. Option C 2.1 m per second in the positive Y direction. And option D 4.01 m per second in the negative Y direction. Now, we've done our diagram for before the collision. Now let's add after the collision and this is where we're looking for that information. And after the collision, we're told that the sailboat stops moving. So we're gonna have our sailboat that's gonna have a final velocity VFS of 0 m per second. And then we have our remote control boat and we wanna know the final speed of this. OK. So we wanna find VF and we're asked for the speed and direction. So we're really looking for the velocity there and they're gonna have the same mass after the collision. They're not gonna, the mass is not gonna change. Now, we have a collision, we're gonna assume there are no net external forces acting. That means we have a conservation of momentum. If we have a conservation of momentum, that means the initial momentum P not is gonna be equal to the final momentum P. Now, our momentum in both the initial and final cases is made up of two components because we have the momentum from the sailboat and the momentum from the remote control. But so what we really have is PNS the initial momentum of the sailboat who was P not B the initial momentum of the boat gonna be equal to PFS. Final momentum of the sailboat was PFB final momentum of the remote controlled vote. Now recall that momentum is given by mass multiplied by velocity. So for each of these terms, corresponding mass multiplied by the corresponding velocity, we get MS VNS who was MB, we not be is equal to MS VFS. What MBVFB? Now the final velocity of this sailboat is zero. That means that its final momentum is zero. That term is going to go to zero. We don't have to worry about it. The rest of the terms we actually have the values for, we know the masses, we know the initial velocities. So the only unknown in our equation is this VFB value that we want to solve. So let's go ahead and substitute in the rest of the values. What we're gonna have is 6.1 kg multiplied by 5.6 m per second. Who was 8.1 kg multiplied by negative 4.1 m per second is going to be equal to 8.1 kg multiplied by VFB. And again, VFB is what we are looking for. Now, we are gonna switch over to using just black. We were using blue for our sail, but we were using green for our remote control boat. Now we're gonna combine these terms. We're gonna switch over to a single color on the left hand side. If we work all of this out, we're gonna have 0.95 kg meters per second. And on the right side, we still have 8.1 kg multiplied by VFB, dividing both sides by 8.1 kg. And we get that VFB, it is going to be equal to approximately 0.1173 m per second. This is a positive value and recall that we've indicated positive to be to the right. So that means our motion is to the right, which is in the positive X direction. So we have now our final speed and direction for the remote controlled boat. If we go to our answer choices and we round to two decimal places like the answer choices. Do we can see that the correct answer is going to be option a 0.12 m per second in the positive X direction. Thanks everyone for watching. I hope this video helped see you in the next one.

A 5.5-kg object moving in the +𝓍 direction at 6.5 m/s collides head-on with an 8.0-kg object moving in the ―𝓍 direction at 4.0 m/s. Determine the final velocity of each object if the 5.5-kg object is at rest after the collision.

Key Concepts

Conservation of Momentum

Momentum Calculation

Elastic vs. Inelastic Collisions

Watch next