8. We have the following differential equations for speeds in the x- and y-directions 公式 Whose solutions are (#f) 公式 9. We use the following initial conditions(使用初值) to determine the drag constant: 公式 根据原有公式 10. We apply the law of conservation of energy(根据能量守恒定律). The work done by the fc 公式 The decrease in potential energy is(势能的减少) 式 he increase in kinetic energy is(动能的增加) 式 Drug acts directly against velocity, so the acceleration vector from drag can be found Newtons awF=maas:(牛顿第二定律) Where a is the acceleration vector and m is mass Using the Newtons Second Law, we have that F/m=a and 公式 公式 Setting the two expressions for tI/t2 equal and cross-multiplying gives 公式 22. We approximate the binomial distribution of contenders with a normal distribution 公式 Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in b gives 公式 As an analytic approximation to for k=l, we get B=c 26. Integrating,(使结合) we get PVT= constant,. where The main composition of the air is nitrogen and oxygen, so i=5 and r=1. 4, so 23. According to First Law of Thermodynamics, we get 公式 Where( ) we also then have Where P is the pressure of the gas and v:公式 V is the volume We put them into the Ideal gas Internal Formula: 公式 Where8．We have the following differential equations for speeds in the x- and y- directions: 公式 Whose solutions are （解） 公式 9．We use the following initial conditions ( 使用初值 ) to determine the drag constant: 公式 根据原有公式 10．We apply the law of conservation of energy（根据能量守恒定律）. The work done by the forces is 公式 The decrease in potential energy is （势能的减少） 公式 The increase in kinetic energy is (动能的增加) 公式 Drug acts directly against velocity, so the acceleration vector from drag can be found Newton’s law F=ma as : (牛顿第二定律) Where a is the acceleration vector and m is mass Using the Newton’s Second Law, we have that F/m=a and 公式 So that 公式 Setting the two expressions for t1/t2 equal and cross-multiplying gives 公式 22．We approximate the binomial distribution of contenders with a normal distribution: 公式 Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in B gives 公式 As an analytic approximation to . for k=1, we get B=c 26．Integrating, （使结合）we get PVT=constant, where 公式 The main composition of the air is nitrogen and oxygen, so i=5 and r=1.4, so 23．According to First Law of Thermodynamics, we get 公式 Where ( ) . we also then have 公式 Where P is the pressure of the gas and V is the volume. We put them into the Ideal Gas Internal Formula: 公式 Where