Physics Problem: Mobile Movement Analysis
Hey guys, let's break down this physics problem. We've got two mobiles, A and B, and their movements are described in a way that's perfect for a little bit of kinematic fun. We'll use some fundamental physics principles to solve this. Essentially, we are going to figure out how these mobiles move and interact with each other. This will involve understanding concepts like velocity, time, and direction. So, let's get started with a cool mobile physics adventure! The problem statement is: A mobile (A) moves at a speed of 10 meters per second. After 7 seconds, mobile B starts moving in the same direction with a speed of 40 meters per hour. Let's see how we can address this!
Understanding the Basics: Velocity and Units
Alright, before we dive in, let's make sure we're all on the same page regarding some core physics concepts. We're dealing with velocity here, which is the speed of an object in a particular direction. It's a vector quantity, meaning it has both magnitude (speed) and direction. In this problem, both mobiles move in the same direction, which simplifies things a bit. We must use consistent units for calculations. Mobile A's speed is given in meters per second (m/s), which is a standard unit. But mobile B's speed is given in kilometers per hour (km/h). So, we'll need to convert everything into the same unit system, which is typically meters per second (m/s) in physics problems. Converting units is a super important skill in physics, as it ensures that our calculations are accurate. We can convert kilometers per hour to meters per second by multiplying by 1000 (to convert kilometers to meters) and dividing by 3600 (to convert hours to seconds). This process ensures we're comparing apples to apples and that our results are meaningful. It's all about keeping track of what you're measuring and making sure everything lines up! Let's get this unit conversion done first so we can continue with the problem.
Step-by-Step Solution: Mobile A's Movement
Let's get into it! First off, let's focus on mobile A. Mobile A moves at a constant velocity of 10 m/s. Since we know the velocity and the time elapsed, we can calculate the distance traveled by mobile A during the first 7 seconds before mobile B even starts moving. We use the fundamental kinematic equation: distance = velocity × time. In this case, the distance covered by mobile A is easily calculated: 10 m/s * 7 s = 70 meters. This is crucial because when mobile B begins its journey, mobile A already has a head start. The distance traveled by mobile A in those 7 seconds creates an initial separation that mobile B must overcome. So, during the initial 7 seconds, mobile A goes 70 meters. We’ll use this as a starting point. Now let's switch our gears and see how mobile B moves.
Calculating Mobile B's Speed in m/s
Alright, now we have to work on the units. Mobile B moves at 40 kilometers per hour, but we need to convert that into meters per second. This is where our conversion skills come in. As mentioned before, we need to convert km/h to m/s. Let's do this step-by-step to make sure we get it right. First, we convert 40 kilometers to meters: 40 km * 1000 m/km = 40,000 meters. Next, we convert one hour into seconds: 1 hour * 3600 seconds/hour = 3600 seconds. Finally, we calculate the speed of mobile B in m/s: 40,000 meters / 3600 seconds ≈ 11.11 m/s. So, mobile B is moving at approximately 11.11 m/s. Now that we've got the units sorted out, we can proceed with the problem more accurately. Remember, the devil is in the details, and keeping track of your units is one of the most important details in physics!
Finding the Time and Distance When Mobile B Catches Mobile A
This is the core of the problem: When does mobile B catch up to mobile A? To solve this, we need to consider the relative motion between the two mobiles. The critical insight is that mobile B needs to cover the initial 70-meter gap created by mobile A's head start. Let's denote the time it takes for mobile B to catch mobile A as 't'. In this time, mobile B will travel a certain distance, and mobile A will travel an additional distance. We know that the distance traveled by mobile A is the initial distance plus the extra distance it travels during time 't'. The distance traveled by mobile B must equal the distance traveled by mobile A in the same amount of time 't'. Since the speed of mobile B is greater than that of mobile A, it will eventually catch up. The distance traveled by each mobile is equal to its velocity multiplied by time. So, we can set up an equation. Let's say that 'x' is the time mobile B moves before catching mobile A. The distance traveled by mobile A is 70 + 10x, and the distance traveled by mobile B is 11.11x. We set those equations equal to each other because the distances have to be the same when mobile B catches up to mobile A. Therefore, 70 + 10x = 11.11x. We then solve for x to find out the total time. Once we have 'x', we can find the distance. This allows us to calculate the time and distance at which the two mobiles meet.
Solving the Equation and Finding the Solution
Now, let's solve the equation. We have the equation 70 + 10x = 11.11x. To solve for 'x', we first subtract 10x from both sides: 70 = 1.11x. Next, we divide both sides by 1.11: x ≈ 63.06 seconds. So, mobile B catches mobile A approximately 63.06 seconds after mobile B starts moving. The total time elapsed since mobile A started moving is then 7 seconds (initial time) + 63.06 seconds = 70.06 seconds. To find the distance at which they meet, we can use the time 'x' and the velocity of either mobile. Using mobile A's velocity, the distance traveled is approximately 10 m/s * 70.06 s ≈ 700.6 meters. Alternatively, using the relative velocities, the distance traveled by mobile B is approximately 11.11 m/s * 63.06 s ≈ 700.6 meters. Therefore, mobile B catches mobile A approximately 700.6 meters from the starting point of mobile A, and this occurs about 70.06 seconds after mobile A began moving. This detailed breakdown is all about breaking down the problem step-by-step, and understanding how each concept interacts with each other.
Final Thoughts and Summary
So, there you have it, guys! We successfully analyzed the motion of two mobiles, calculated their velocities, and determined when and where mobile B catches up to mobile A. We navigated the conversion of units, accounted for the initial conditions, and applied basic kinematic equations. The key takeaways are understanding the concepts of velocity, time, distance, and unit conversion. This problem is a good example of how physics uses math to predict how things move. Always remember to break down the problem into smaller, manageable steps. Always start by identifying what's given, what you need to find, and the relevant formulas. Pay close attention to units, and don't hesitate to draw diagrams to visualize the situation. The more you practice, the more comfortable you'll become with solving these kinds of problems. Keep up the awesome work, and keep exploring the fascinating world of physics! Keep in mind that physics is all about understanding how the world works, and this example is just one step of many in your journey. Keep asking questions, keep learning, and keep having fun with physics!
