A package of medical supplies is released from a small airpllane flying a mercy mission over an isolated jungle settlement. The plane flies horizontally with a speed of 20 m/s and an altitude of 20 meters. How far from the release point will the package strike the ground?
IT goes down 20 meters.
Horizontal= 20m/s*timeinair
to get time in air,
20m=1/2 g t^2 or t= sqrt 2*10/9.8 sec
To determine the distance from the release point at which the package will strike the ground, we need to use the equations of motion. In this case, since the airplane is flying horizontally, there won't be any vertical acceleration.
First, let's find the time it takes for the package to hit the ground using the equation:
h = ut + (1/2)gt^2
Where:
h = initial altitude = 20 meters
u = initial vertical velocity = 0 m/s (since the package is dropped, not thrown)
g = acceleration due to gravity = 9.8 m/s^2
t = time
Rearranging the equation to solve for time (t), we get:
t = sqrt((2h)/g)
Substituting the values, we have:
t = sqrt((2 * 20) / 9.8)
t ≈ sqrt(4.08)
t ≈ 2.02 seconds (rounded to two decimal places)
Now that we know the time it takes for the package to hit the ground, we can calculate the horizontal distance traveled by the airplane using the equation:
d = v * t
Where:
d = horizontal distance
v = horizontal velocity = 20 m/s (given)
t = time = 2.02 seconds (from the previous calculation)
Plugging in the values, we get:
d = 20 * 2.02
d ≈ 40.4 meters
Therefore, the package will strike the ground approximately 40.4 meters from the release point.