5. Elaine shoots a bullet straight up in the air from a gún. It reaches a height of 1940 m. How fast was the bullet fired? __ 6. 'How long is the bullet in #5 in the air before it hits the ground again?

**5.**<br /><br />Here's how to calculate the initial velocity of the bullet:<br /><br />* **Understanding the physics:** When the bullet reaches its maximum height, its final velocity is 0 m/s. We can use the following kinematic equation:<br /><br /> v² = u² + 2as<br /><br /> Where:<br /> * v = final velocity (0 m/s)<br /> * u = initial velocity (what we want to find)<br /> * a = acceleration due to gravity (-9.8 m/s², negative since it acts downwards)<br /> * s = displacement (1940 m)<br /><br />* **Solving for u:**<br /><br /> 0 = u² + 2 * (-9.8) * 1940<br /> u² = 38024<br /> u = √38024 <br /> u ≈ 195 m/s<br /><br />Therefore, the bullet was fired at approximately 195 m/s.<br /><br /><br />**6.**<br /><br />Here's how to calculate the total time the bullet is in the air:<br /><br />* **Time to reach maximum height:** We can use the following kinematic equation:<br /><br /> v = u + at<br /><br /> Where:<br /> * v = final velocity (0 m/s)<br /> * u = initial velocity (195 m/s)<br /> * a = acceleration due to gravity (-9.8 m/s²)<br /> * t = time (what we want to find)<br /><br /> 0 = 195 + (-9.8)t<br /> 9.8t = 195<br /> t ≈ 19.9 s<br /><br />* **Total time in the air:** The time it takes for the bullet to fall back down is equal to the time it took to reach its maximum height. Therefore, the total time in the air is twice the time to reach the maximum height:<br /><br /> Total time = 2 * 19.9 s ≈ 39.8 s<br /><br />Therefore, the bullet is in the air for approximately 39.8 seconds.<br />