Final answer:
The dart is in the air for approximately 0.904 seconds.
Step-by-step explanation:
To calculate the time the dart is in the air, we can use the equations of motion. The vertical distance traveled by the dart can be found using the equation:
s = ut + (1/2)gt²
where s is the vertical distance, u is the initial vertical velocity, t is the time, and g is the gravitational acceleration.
Given that the dart is fired from a height of 1m and lands 5m downrange, the vertical distance traveled is equal to the initial height minus the final height (-4m).
From this, we can plug in the known values to find the time:
-4 = 0 + (1/2)(9.8)t²
Simplifying, we get:
t²= 0.816
Taking the square root of both sides:
t = 0.904 seconds
Therefore, the dart is in the air for approximately 0.904 seconds.