An airplane is flying horizontally with a constant velocity of 160 m/s at an altitude of 5100 m when it releases a package.
a. How long does it take for the package to reach the ground? (Ignore air resistance.)
b. What is the distance between the airplane and the package when the package hits the ground? Ignore air resistance.
c. How far ahead of the target along the x direction should the plane be when it releases the package? (Again, ignore air resistance.)
a. h=sqrt(1/2 g t^2_
solve for t.
b. distance=time*160m/s that is horizonal distance. Slant distance is
slant distance=sqrt(5100^2+horizontalDistanc^2)
c.what was horizontal distance in b?
To answer these questions, we need to consider the horizontal and vertical motions of the package separately.
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 = u * t + (1/2) * a * t^2
Where:
h = change in vertical position (altitude)
u = initial vertical velocity (0 m/s, as the package is initially at rest)
t = time taken
a = acceleration due to gravity (-9.8 m/s^2, acting downwards)
Rearranging the equation, we get:
t = √(2h / -a)
Given the initial altitude (h) of the package is 5100 m, and the acceleration due to gravity (a) is -9.8 m/s^2, we can plug in the values and solve for t.
t = √(2 * 5100 / -9.8) ≈ 31.6 seconds
Therefore, it takes approximately 31.6 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 also undergoes horizontal motion with a constant velocity.
Since velocity = distance / time, we can calculate the horizontal distance using the formula:
distance = velocity * time
Given that the horizontal velocity of the airplane is 160 m/s and the time taken for the package to reach the ground from part (a) is 31.6 seconds, we can calculate the distance.
distance = 160 m/s * 31.6 s ≈ 5,056 meters
Therefore, the distance between the airplane and the package when the package hits the ground is approximately 5,056 meters.
c. How far ahead of the target along the x direction should the plane be when it releases the package?
Since the airplane is flying horizontally with a constant velocity and the package is released from it, the horizontal position of the package will be the same as that of the airplane at the moment of release.
So, the distance ahead of the target along the x direction that the plane should be would depend on the time taken for the package to reach the ground.
From part (a), we know that the time taken for the package to reach the ground is approximately 31.6 seconds.
Using the horizontal velocity of the airplane (160 m/s) and the time taken for the package to reach the ground (31.6 seconds), we can calculate the distance.
distance = velocity * time
distance = 160 m/s * 31.6 s ≈ 5,056 meters
Therefore, the airplane should be approximately 5,056 meters ahead of the target along the x direction when it releases the package.