Experiment 5 projectile motion (comprehensive test)

Introduction Mathematica can be used to explore various possibilities, so as to simulate what is going on under given assumptions.

Find an answer to a math problem. The problem discussed below is a sample experiment about projectile flight, specifically the motion of projectile without air resistance. We intend to use such an example to let readers know how to explore a solution to a mathematical problem. When you write an experimental report, you must clearly explain what you did and why you did it, and gradually get familiar with the writing methods of scientific reports.

According to the reconnaissance, it is found that there are enemy tanks in front of the horizontal distance 10km of our artillery position.

50km is coming to our position, and now we will fire shells to destroy enemy tanks. In order to effectively destroy enemy tanks in the shortest time, it is necessary to

Each gun can shoot accurately, so the problem can be simplified to the problem of shooting a mobile tank accurately with a single gun. Hypothetical shell

The firing rate can be controlled between 0.2 km/s and 0.6 km/s, and you can choose any firing rate and firing angle.

Destroy enemy tanks most effectively.

The results show that if air resistance is not considered, the trajectory of projectile is determined by parameter equation.

,

Given, where are the initial velocity of the projectile, the launching angle of the projectile and the acceleration of gravity (9.8m/). The first square above.

The equation describes the horizontal position of the shell at this moment, while the second equation describes the vertical position of the shell at this moment.

Assume that the artillery is located at the coordinate origin (), with the axis vertically upward and the axis horizontally pointing to the enemy tank. Below.

First, use Mathematica drawing command to display the typical trajectory of the projectile. invest

horiz[v_，a_，t_]:=v Cos[a Pi/ 180] t

vert[v_，a_，t _]:= v sin[a pi/ 180]t-( 1/2)g t^2

g=9.8

Assume that the initial velocity of the shell is 0.25km/s, the launching angle is, and the input is

parameter plot[{ horiz[250，65，t]，vert[250，65，t]}，

{t，0，50}，plot range-& gt； {0，5000}，axes label-& gt； {x，y}]

Get the typical figure of projectile trajectory (Figure 5- 1):

Figure 5- 1

laboratory report

Under the above assumptions, further study the following issues:

(1) Select an initial velocity and launch angle, and draw the trajectory of the projectile with Mathematica.

(2) Assuming that the tank is stationary in front of the gun 10km and the initial velocity of the shell is 0.32km/s, what kind of bomb should be selected?

You have to shoot at an angle to hit the tank? Draw a few bullet trajectory diagrams, and illustrate the rationality of your conclusion through experimental data and graphics.

(3) Assuming that the tank is stationary in front of the gun 10km, under the condition of exploring to reduce or improve the initial velocity of the shell, it should be

How to choose the firing angle of shells? Through the above discussion, the most reasonable and effective launching speed and angle are summarized.

(4) On the basis of the above conclusions, continue to explore, assuming that the tank is in front of the artillery 10km, and the speed is 50km/h in the direction of the artillery.

Forward, how to make a plan to quickly destroy enemy tanks at this time?