The horizontal distance traveled by the parcel in this time is approximately 581.6 meters.
Given - Initial horizontal speed of the airplane (u) = 80 m/s
Altitude (h) = 260 m
Acceleration due to gravity (g) = 9.8 m/s^2
To find - the horizontal distance traveled by the parcel in this time
Solution -
First, let's calculate the time (t) it takes for the parcel to reach the ground:
Using the equation for vertical motion:
h = ut + (1/2)gt^2
Rearranging the equation and substituting the known values:
260 = 0t + (1/2)(9.8)t^2
Rearranging again:
4.9t^2 = 260
Dividing both sides by 4.9:
t^2 = 52.94
Taking the square root of both sides:
t ≈ 7.27 s
Therefore, it takes approximately 7.27 seconds for the parcel to strike the ground.
Next, let's calculate the horizontal distance (d) traveled by the parcel in this time:
Using the equation for horizontal motion:
d = ut
Substituting the known values:
d = 80 m/s * 7.27 s
d ≈ 581.6 m
Therefore, the horizontal distance traveled by the parcel is approximately 581.6 meters.