Final answer:
For a bullet fired at a 45-degree angle with an initial velocity of 490 m/s, the time to reach the maximum height is 35.35 seconds, and the maximum height achieved is 6202.45 meters.
Step-by-step explanation:
When a hunter fires a bullet at an angle of 45 degrees with an initial velocity of 490 meters per second, the time taken to reach the maximum point and the maximum height can be calculated using kinematic equations for projectile motion.
Since the angle of launch is 45 degrees, the initial velocity can be evenly divided into horizontal and vertical components. This key feature simplifies the calculations as both components will have the same magnitude.
To calculate the time to reach the maximum height, we use the vertical component of the initial velocity. The vertical component (v_y) is found by multiplying the initial velocity by sin(45°), which is
490 m/s * sin(45°) = 490 m/s * 0.7071 ≈ 346.48 m/s.
The time (t) taken to reach the maximum point is found by dividing this vertical component by the acceleration due to gravity (g=9.8 m/s^2), hence
t = v_y / g ≈ 346.48 m/s / 9.8 m/s^2 ≈ 35.35 seconds.
The maximum height (H) is found using the equation H = (v_y²) / (2*g), which results in
H = (346.48 m/s)² / (2*9.8 m/s^2) ≈ 6202.45 meters.
Therefore, the time taken to reach the maximum point is 35.35 seconds and the maximum height reached is 6202.45 meters.