A boy throws a ball with a velocity of 15 m/s at an angle of 15° with the horizontal. The distance at which the ball strikes the ground is

Options

A. 5 m
B. 20 m
C. 10 m
D. 11.25 m

Answer

To find the distance at which the ball strikes the ground when thrown with a velocity of 15 m/s at an angle of 15° with the horizontal, we can use the formula for the range of projectile motion.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial velocity (u) = 15 m/s
- Angle of projection (θ) = 15°
- Acceleration due to gravity (g) = 10 m/s² (approximate value)

2. **Use the Range Formula:**
The formula for the range (R) of a projectile is given by:
\[ R = \frac{u^2 \sin(2\theta)}{g} \]

3. **Calculate sin(2θ):**
First, we need to calculate \(2\theta\):
\[ 2\theta = 2 \times 15° = 30° \]
Now, find \(\sin(30°)\):
\[ \sin(30°) = \frac{1}{2} \]

4. **Substitute Values into the Range Formula:**
Now, substitute the values into the range formula:
\[ R = \frac{(15)^2 \cdot \sin(30°)}{10} \]
\[ R = \frac{225 \cdot \frac{1}{2}}{10} \]

5. **Calculate the Range:**
Simplifying the expression:
\[ R = \frac{112.5}{10} = 11.25 \text{ meters} \]

6. **Conclusion:**
The distance at which the ball strikes the ground is 11.25 meters.

### Final Answer:
The ball will hit the ground after it covers a distance of 11.25 meters.

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