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确定目标距离处的最终速度

physics python-3.x python

user7884512 · 技术社区 · 8 年前

在我使用Python开发的这个程序中,目标是在给定的初始速度、角度以及结构的距离/高度上获取用户输入。我已经能够计算出物体到达目标所需的时间,但我不确定为什么最终速度(到达目标时的速度)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.')

输入速度:20 输入角度:40 输入距离:25 结构输入高度:15

预期输出

到达结构的时间:1.63176秒

我的程序输出

到达结构的时间:1.63176

最终速度:15.36755

乍一看,我的程序似乎非常接近,所以我怀疑有舍入错误,但这仅仅是与所选数字接近的巧合。

1 回复 | 直到 8 年前

Spherical Cowboy 8 年前

你算错了 horizontal and vertical components 最终速度。只使用角度的余弦和正弦,而不是(初始速度的幅值)分别乘以余弦和正弦。如果修改以下两行代码,您将获得您所提供的示例输入所需的结果:

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

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!')