在目標距離確定最終速度

Question

在這個程序中，我一直在與Python合作，目標是在給定的初始速度，角度以及結構距離多遠/我們'重新瞄準。我已經能夠計算出達到某個目標需要多長時間，但我不知道爲什麼最終速度（它到達目標時的速度有多快）出現錯誤。

# 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.') 

下面是一個示例輸入和預期輸出應該是什麼：

輸入速度：20 輸入角度：40 輸入距離：結構25 輸入身高：15

預期產量：

達到結構的時間：1.63176 s

末速度：15.6384小號

我的程序的輸出：

時間達到結構：1.63176

末速度：15.36755

乍一看它會出現在我的計劃是非常關閉，所以我懷疑是一個舍入誤差，但它與選擇的數字很接近。

Answer 1

您錯誤計算了最終速度的horizontal and vertical components。你只使用角度的餘弦和正弦，而不是初始速度（的幅度）乘以餘弦和正弦。如果你修改的代碼如下兩行，你會得到你要找的結果給你提供的樣品輸入：

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

我改寫了你原來的代碼位，而且還計算出最終的高度，以檢查是否結構被擊中與否，因此，如有需要隨時使用它：

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!')