To determine how far the firework will travel before reaching the ground, we need to solve the equation:
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
This can be rewritten as:
\[ 0 = -\frac{25}{36}x^2 + \frac{50}{3}x \]
To clear the fraction, we can multiply the entire equation by 36:
\[ 0 = -25x^2 + 600x \]
Now, we can rewrite the equation:
\[ 25x^2 - 600x = 0 \]
Next, we can factor out \( 25x \):
\[ 25x(x - 24) = 0 \]
This gives us two solutions:
- \( 25x = 0 \) which results in \( x = 0 \)
- \( x - 24 = 0 \) which results in \( x = 24 \)
Since the problem is asking for the value of \( x \) when the firework reaches the ground, we find that:
The firework will travel 24 feet before reaching the ground.
Thus, the correct answer is A: 24 feet.