# Projections
df["SinDir"] = np.sin(df["Dir"])
df["CosDir"] = np.cos(df["Dir"])

# Projected speeds
df['SpeedX'] = df['S'] * df['CosDir']
df['SpeedY'] = df['S'] * df['SinDir']

# Expected positions
for i in range(1, 4):
    df[f'X_in_{i}_second'] = df['X'] + i*df['SpeedX']
    df[f'Y_in_{i}_second'] = df['Y'] + i*df['SpeedY']