An airplane is flying horizontally with a constant velocity of 170 m/s at an altitude of 4500 m when it drops a package.
(a) How long does it take for the package to reach the ground?
___s
(b) What is the distance between the airplane and the package when the package hits the ground? Ignore air resistance.
___m
(c) How far ahead of the target along the x direction should the plane be when it releases the package?
___m
How long does it take for something to fall 4500 m (neglecting terminal velocity)?
horizontally, 170*time is horizontal distance covered.
a)26s b)
To solve these problems, we can use the equations of motion and the principles of projectile motion. Let's break down each part of the problem to find the answers:
(a) How long does it take for the package to reach the ground?
To find the time it takes for the package to reach the ground, we can use the equation of motion for vertical motion:
h = ut + (1/2)gt^2
Where:
h is the initial height of the package (4500 m)
u is the initial velocity of the package in the vertical direction (0 m/s since it's dropped)
g is the acceleration due to gravity (-9.8 m/s^2)
t is the time it takes for the package to reach the ground (what we're solving for)
Substituting the values into the equation, we get:
4500 = 0*t + (1/2)*(-9.8)*t^2
Simplifying the equation, we have:
4.9t^2 = 4500
Dividing both sides by 4.9 and taking the square root, we can solve for t:
t = √(4500/4.9)
Using a calculator, we find t ≈ 42.6 seconds.
Therefore, it takes approximately 42.6 seconds for the package to reach the ground.
(b) What is the distance between the airplane and the package when the package hits the ground?
Since the airplane is flying horizontally, the package's horizontal distance from the airplane remains constant throughout its fall. The distance traveled is given by the horizontal velocity multiplied by the time taken:
Distance = Horizontal velocity * Time
Distance = 170 m/s * 42.6 s
Using a calculator, we find that the distance is approximately 7232 meters.
Therefore, when the package hits the ground, the distance between the airplane and the package is approximately 7232 meters.
(c) How far ahead of the target along the x direction should the plane be when it releases the package?
Since the horizontal distance traveled by the package remains constant, the plane needs to be directly overhead the target when the package is dropped. Therefore, the plane should be directly above the target when it releases the package.
Hence, the plane does not need to be ahead of the target in the x-direction; it should be exactly above the target when it releases the package. Therefore, the distance ahead of the target along the x-direction should be zero meters.