To solve this problem, we need to calculate the time taken for the bullet to reach the target using the given information. Here's a breakdown of the known dataTo solve this problem, we need to calculate the time taken for the bullet to reach the target using the given information. Here's a breakdown of the known

• Initial velocity $v_0 = 427 \, \text{m/s}$
• Horizontal distance to the target $d = 91.4 \, \text{m}$
• The problem asks for the time $t$ required for the bullet to reach the target considering the projectile motion at two angles of launch.

We'll assume there are two angles (from the description) that satisfy the projectile motion to hit the target at this distance, and calculate the time taken for both angles using the equations of motion.

The horizontal component of the velocity is given by: $v_x = v_0 \cos \theta$ The time $t$ to reach the target can be found using: $t = \frac{d}{v_x} = \frac{91.4}{v_0 \cos \theta}$

Let me calculate the time for each of the angles. If angles were provided, we could use them directly; otherwise, I'll solve for two possible angles based on the range formula for projectile motion.

Let me compute this.The two possible launch angles for the bullet to reach the target are approximately:

• $\theta_1 \approx 0.14^\circ$
• $\theta_2 \approx 89.86^\circ$

The corresponding times for the bullet to hit the target are:

• For $\theta_1$, the time is approximately $t_1 \approx 0.214 \, \text{seconds}$
• For $\theta_2$, the time is approximately $t_2 \approx 87.05 \, \text{seconds}$

Since $\theta_1$ is much closer to the horizontal, the bullet reaches the target much faster compared to the near-vertical shot at $\theta_2$.

Would you like more details or clarifications on any part? Here are 5 related questions you can explore:

1. How does air resistance affect projectile motion in real-world scenarios?
2. What is the maximum height reached by the projectile for the two angles?
3. How can we calculate the horizontal range of a projectile at any given angle?
4. What happens if the initial velocity changes in this scenario?
5. How would this calculation change if the target was placed at a different height?

Tip: The time of flight in projectile motion primarily depends on the horizontal velocity component, so a small launch angle results in quicker times!