To determine the range of the ball's flight, we can use the projectile motion formula for range:

$R = \frac{{v^2 \sin(2\theta)}}{g}$

where:

• $v = 10 \, \text{m/s}$ (initial speed),
• $\theta = 44^\circ$ (angle of projection),
• $g = 9.8 \, \text{m/s}^2$ (acceleration due to gravity).

Step-by-Step Calculation

1. Calculate $\sin(2\theta)$: $2\theta = 2 \times 44^\circ = 88^\circ$ Using $\sin(88^\circ) \approx 0.999$.

2. Plug in the values: $R = \frac{{(10)^2 \times 0.999}}{9.8}$

3. Solve for $R$: $R = \frac{100 \times 0.999}{9.8} \approx \frac{99.9}{9.8} \approx 10.2 \, \text{m}$

Based on the available options, the correct answer is approximately 10 m.

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions to explore further:

1. What would happen to the range if the angle were increased to 60 degrees?
2. How would air resistance affect the range of the projectile?
3. What is the maximum height reached by the ball in this scenario?
4. How would the range change if the initial speed were doubled?
5. What would be the range if the ball were thrown on a planet with a different gravity?

Tip: In projectile motion, the maximum range occurs at a launch angle of 45 degrees, given no air resistance.