确定目标距离处的最终速度

Question

在这个程序中，我一直在与 Python 合作，目标是根据给定的初始速度、角度以及结构 is/how 的高度获取用户输入的目标。我已经能够计算出某物到达目标需要多长时间，但我不确定为什么最终速度（到达目标时的速度）会出现错误。

# User inputs
velocity = float(input('Give me a velocity to fire at (in m/s): '))
angle = float(input('Give me an angle to fire at: '))
distance = float(input('Give me how far away you are from the 
structure: '))
height = float(input('Give me the height of the structure (in meters): 
'))
slingshot = 5 #Height of slingshot in meters
gravity = 9.8 #Earth gravity

# Converting angles to radians
angleRad = math.radians(angle)

# Computing our x and y coordinate
x = math.cos(angleRad)
y = math.sin(angleRad)

# Calculations
time = distance/(velocity * x)
vx = x
vy = y + (-9.8 * time)
finalVelocity = math.sqrt((vx ** 2) + (vy ** 2))   

# Output of program
print('It takes your bird' , time , 'seconds to reach the structure')
print('Your velocity at the target distance is' , finalVelocity , 
'meters per second.')

这是一个示例输入以及预期输出应该是什么：

输入速度：20 输入角度：40 输入距离：25 输入结构高度：15

预期输出：

到达结构的时间：1.63176 秒

最终速度：15.6384 s

我程序的输出:

到达结构的时间：1.63176

最终速度：15.36755

乍一看，我的程序似乎很接近，所以我怀疑是舍入错误，但这只是与所选数字接近的巧合。

Answer 1

你计算错了最终速度的horizontal and vertical components。您只使用了角度的余弦和正弦，而不是初始速度（的大小）分别乘以余弦和正弦。如果您修改以下两行代码，您将根据您提供的示例输入获得您正在寻找的结果：

vx = velocity * x
vy = velocity * y - 9.8 * time

我稍微重写了你的原始代码，并计算了最终高度以检查结构是否被击中，所以如果需要请随意使用它：

import math

# User inputs
# v0 = float(input('Give me a velocity to fire at (in m/s): '))
# angle = float(input('Give me an angle to fire at: '))
# distance = float(input('Give me how far away you are from the structure: '))
# height_structure = float(input('Give me the height of the structure (in meters):'))

# Test inputs
v0 = 20
angle = 40
distance = 25
height_structure = 15

# Constants
height_slingshot = 5  # Height of slingshot in meters
g = 9.8  # Earth gravity

# Converting angle to radians
angleRad = math.radians(angle)

# Computing initial velocity components
vx0 = v0 * math.cos(angleRad)
vy0 = v0 * math.sin(angleRad)

# Computing time to travel horizontal distance
t_x = distance / vx0

# Computing final vertical velocity component
vy_final = vy0 - g * t_x

# Computing magnitude of final velocity
v_final = math.sqrt((vx0 ** 2) + (vy_final ** 2))
# Note: Horizontal component is constant

# Computing final height
y_final = height_slingshot + vy0 * t_x - g / 2 * t_x ** 2

# Verify if t_x was computed correctly
# t_y1 = (vy0 + math.sqrt(vy0 ** 2 - 2 * g * y_final)) / g
# t_y2 = (vy0 - math.sqrt(vy0 ** 2 - 2 * g * y_final)) / g

# Output of program
print('It takes your bird', t_x, 'seconds to reach the structure.')
print('Your velocity at the target distance is', v_final,
      'meters per second.')

print('\nFinal height:    ', y_final)
print('Structure height:', height_structure)
if 0. <= y_final <= height_structure:
    print('\nYou hit the structure!')
elif y_final < 0:
    print('\nYou missed. Not far enough!')
else:
    print('\nYou missed. Too far!')

确定目标距离处的最终速度

Determining final velocity at a target distance

python

physics

python-3.x