A helicopter is flying in a straight line over a level field at a constant speed of 6.2 m/s and at a constant altitude of 11.3 m. A package is ejected horizontally from the helicopter with an initial velocity of 14.0 m/s relative to the helicopter, and in a direction opposite the helicopter's motion. Find the initial velocity of the package relative to the ground.
To find the initial velocity of the package relative to the ground, we will break down the velocities and use vector addition.
Let's first analyze the helicopter's velocity. The helicopter is moving in a straight line at a constant speed of 6.2 m/s. Since the altitude of the helicopter remains constant, we can ignore the vertical component of its velocity.
Now, let's analyze the package's velocity relative to the helicopter. The package is ejected horizontally with an initial velocity of 14.0 m/s in the opposite direction of the helicopter's motion. Therefore, the package's horizontal velocity relative to the ground is also 14.0 m/s (opposite direction of the helicopter).
To find the package's overall initial velocity relative to the ground, we can add the helicopter's velocity and the package's velocity relative to the helicopter using vector addition.
Since the helicopter's velocity is only in the horizontal direction, we can ignore the vertical component of the helicopter's velocity. So, we can add the horizontal velocities.
The helicopter's horizontal velocity: 6.2 m/s
The package's horizontal velocity relative to the helicopter: -14.0 m/s (opposite direction)
Adding these velocities: 6.2 m/s + (-14.0 m/s) = -7.8 m/s (opposite direction)
Therefore, the initial velocity of the package relative to the ground is -7.8 m/s in the direction opposite to the helicopter's motion.
To find the initial velocity of the package relative to the ground, we need to consider the velocities of both the helicopter and the package.
Since the package is ejected horizontally from the helicopter, its vertical velocity is the same as the helicopter's vertical velocity, which is 0 m/s (constant altitude).
Now, let's determine the horizontal velocity of the package relative to the ground. The package has an initial velocity of 14.0 m/s relative to the helicopter in the opposite direction of the helicopter's motion.
The helicopter is moving at a constant speed of 6.2 m/s, so the horizontal component of its velocity is also 6.2 m/s.
To find the initial velocity of the package relative to the ground, we need to add the horizontal velocities of the helicopter and the package.
So, the initial velocity of the package relative to the ground is:
Horizontal component: 6.2 m/s (helicopter's velocity) - 14.0 m/s (package's velocity) = -7.8 m/s
Therefore, the initial velocity of the package relative to the ground is -7.8 m/s, in the opposite direction of the helicopter's motion.