Final answer:
Using the physics of projectile motion and the formula for vertical displacement, the arrow was determined to be fired from approximately 1.54 meters above the ground.
Step-by-step explanation:
The question relates to projectile motion, specifically calculating the height from which an arrow was fired based on the time it was in the air before hitting the ground. The arrow was fired horizontally at a speed of 41 m/s and was in the air for 0.56 seconds. To find the height from which the arrow was fired, we can use the formula for the vertical displacement in projectile motion:
h = ½ g t^2
where h is the height, g is the acceleration due to gravity (9.8 m/s^2 on Earth), and t is the time the arrow was in the air. Plugging in the given values:
h = ½ * 9.8 m/s^2 * (0.56 s)^2
h = 0.5 * 9.8 * 0.3136
h = 1.53968 m
Therefore, the arrow was fired from a height of approximately 1.54 meters above the ground.
In projectile motion, the horizontal and vertical motions are independent of each other. To find the height at which the arrow was fired, we need to find the vertical distance traveled in the given time.
Given that the arrow traveled for 0.56 s and its horizontal velocity is 41 m/s, we can use the formula:
Vertical distance (h) = 0.5 * acceleration * time^2
Since the arrow was fired horizontally, its initial vertical velocity is 0 m/s. Therefore, the acceleration is equal to the acceleration due to gravity (9.8 m/s^2).
Plugging in the values, we get:
h = 0.5 * 9.8 * (0.56)^2
Simplifying:
h = 0.5 * 9.8 * 0.3136
h = 1.5376 m
Therefore, the arrow was fired from a height of approximately 1.54 meters.