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The problem in the image involves projectile motion, where Yusuf needs to shoot a pellet at a target located 10 meters away, with an initial velocity of \( v_0 = 150 \, \text{m/s} \). The goal is to determine the angle \( \theta \) at which Yusuf should aim above the horizontal to account for gravity.

### Solution Outline:

1. **Projectile motion basics**:
   - The horizontal range \( R \) of a projectile is given by the formula:
     \[
     R = \frac{v_0^2 \sin(2\theta)}{g}
     \]
     where:
     - \( R \) is the horizontal distance to the target (10 m in this case),
     - \( v_0 \) is the initial velocity (150 m/s),
     - \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
     - \( \theta \) is the angle above the horizontal.

2. **Rearrange the formula** to solve for \( \theta \):
   - From the formula above, solve for \( \theta \) by first isolating \( \sin(2\theta) \):
     \[
     \sin(2\theta) = \frac{R \cdot g}{v_0^2}
     \]
   - Substitute the given values:
     \[
     \sin(2\theta) = \frac{10 \cdot 9.81}{150^2}
     \]
     \[
     \sin(2\theta) \approx \frac{98.1}{22500}
     \]
     \[
     \sin(2\theta) \approx 0.00436
     \]
   - Solve for \( 2\theta \):
     \[
     2\theta = \sin^{-1}(0.00436)
     \]
     \[
     2\theta \approx 0.2497^\circ
     \]
   - Therefore:
     \[
     \theta \approx \frac{0.2497^\circ}{2} = 0.1249^\circ
     \]

### Conclusion:
Yusuf should aim at an angle of approximately **0.125°** above the horizontal in order to hit the target that is 10 meters away.

Would you like more details or have any questions about this calculation? Here are 5 additional questions that build on this concept:

1. How would the angle change if the distance to the target doubled?
2. What would the angle be if the initial velocity was reduced to 100 m/s?
3. Can you calculate the total time the pellet is in the air before it hits the target?
4. How would air resistance affect this calculation in a real-world scenario?
5. What would happen if the angle were higher than the calculated value?

**Tip**: When solving projectile motion problems, always consider breaking the motion into horizontal and vertical components for clearer calculations.

In his second shot, Yusuf readjusts his aim by shooting the pellet at an angle θ above the horizontal in order to account for the influence of gravity. At what angle θ should Yusuf shoot the pellet in order to hit a bullseye 10 m away? Assume the pellet’s initial velocity is 150 m/s.

Calculate the angle θ needed for Yusuf to hit a bullseye 10 meters away with a pellet shot at 150 m/s, factoring in gravity's influence. This problem covers essential concepts in projectile motion, trigonometry, and physics. Ideal for high school physics students.

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