Final answer:
Using the gravitational formula for height, the projectile launched horizontally at 2.6 m/s from a height and falling after 3.1 seconds was launched from approximately 47.1 meters above ground.
Step-by-step explanation:
The student has asked how to calculate the height from which a projectile is launched if it is launched horizontally at 2.6 m/s and falls to the ground 3.1 seconds later. To find the height the projectile was launched from, we can use the equations of projectile motion.
Since the projectile was launched horizontally, the initial vertical velocity is 0 m/s.Using the formula for the distance fallen under gravity, which is h = (1/2)g t^2, where g is the acceleration due to gravity (approximately 9.81 m/s^2), and t is the time in seconds, we can determine the height of the launch.
In this case, h = (1/2) * 9.81 m/s^2 * (3.1 s)^2. Calculating this gives us h = (1/2) * 9.81 * 9.61 which equals 47.1455 m. Thus, the height from which the projectile was launched is approximately 47.1 meters above ground.