1. What does the demonstration dart method mean?
Mathematically, there are three ways to prove the dart model: 1, and geometric method: this is the most basic method, and the dart model is proved by geometric shape and angle. The dart model consists of triangles and parabolas, which can be proved by geometric methods. 2. Physical method: This method uses the physical laws involved, such as air resistance, gravity and speed, to prove the dart model.
Method 1: Mathematical deduction
First of all, we can prove the correctness of the darts model through mathematical deduction. Suppose we have a dart model with a tip length of A, a tail length of B, the distance from the center of gravity to the tip of C, and the distance from the center of gravity to the tail of D. According to the geometric principle, we can get the following relations: a+b = c+d, A * C = B * D.
The specific values of a, b, c and d can be obtained by solving the equation, thus proving that the four parameters of the dart model are interrelated.
Method 2: Physical experiment method
In addition to mathematical deduction, we can also prove the correctness of the dart model through physical experiments. First, we make a dart model with a tip length of A and a tail length of B, and measure the distance from the center of gravity to the tip of C and the distance from the center of gravity to the tail of D. Then, we throw the dart model out. To record the movement of darts with high-speed cameras.
By analyzing the video of high-speed camera, we can get the balanced rotation of the dart model in the air, and verify the relationship of A+B = C+D. At the same time, we can calculate the stability and flight trajectory of the dart by using the mechanical principle, which further proves the correctness of the dart model.
Method 3: Numerical simulation method
Before actually making the dart model, numerical simulation can be used to verify its rationality. Firstly, the mathematical model of dart model can be established and appropriate parameters can be set, such as the length of tip, the length of tail and the position of center of gravity. Then, the movement process of darts in the air is simulated by numerical calculation.
By observing the results of numerical simulation, we can judge whether the dart model can keep a balanced and stable rotation and verify the relationship of A+B = C+D. If the numerical simulation results are consistent with the actual situation, we can further make the model.