1. Determine the basic variables: First, determine the basic variables in the problem, such as the speed, starting position and meeting time of two objects. Express it as a symbol or variable in order to establish an equation.
2. Establish a satisfaction equation: according to the satisfaction condition, establish an equation describing the relationship between two objects. Distance = speed × time is usually used to establish equations. Pay attention to their relative movement direction and starting position.
3. Solving the equation: According to the established equation, solving the equation solves the unknown quantity. This may need to be solved by algebraic knowledge, such as collocation method, factorization, quadratic equation solution and so on.
4. Check the answer: check the solved unknown quantity back to the original equation to ensure that the obtained result meets the constraints and requirements of the problem.
5. Pay attention to special circumstances: when solving problems, pay special attention to whether there are special circumstances, such as one of the objects is stationary and the speed is phase. These situations may lead to special solutions or no solutions.
6. Draw a chart to help you understand: Drawing a speed-time chart or a distance-time chart is helpful to better understand the problem and solve the process. The relative position and movement of objects can be seen more intuitively through charts.
7. Setting a frame of reference: It is very important to choose a suitable frame of reference when dealing with relative motion. Usually, an object or person is selected as a fixed reference point and its speed is set to zero, which can simplify the problem and make it easier to establish the equation.
8. Determine the unknown quantity: when establishing the equation, clearly determine the unknown quantity to be solved. This can help you sort out problems more systematically and avoid confusion when solving equations.
Common application scenarios of mathematical encounter problems
1, traffic planning: In traffic planning, mathematical encounter problems can help predict the encounter of different vehicles or pedestrians on the road, thus optimizing traffic flow and reducing traffic congestion.
2. Running competition: Mathematical encounter problem can be used to calculate the meeting time of different athletes on a runway and help the referee determine the result of the competition.
3. Remote sensing and navigation: In remote sensing technology and navigation system, the mathematical encounter problem can be used to calculate the encounter time and path between satellites, planes or drones, and to plan and navigate the flight path.