A helicopter is flying in a straight line over a level field at a constant speed of 21.7 m/s and at a constant altitude of 11.5 m. A package is ejected horizontally from the helicopter with an initial speed of 21.6 m/s relative to the helicopter, and a direction opposite to the helicopter's motion. Find the initial speed of the package relative to the ground.
I thought I knew how to do this...until I saw that they give an altitude. Can someone give me the first steps? I can probably get it after that.
The altitude has nothing to do with intial speed.
Vrelative ground= Vhelo+ Vrelathelo
= 21.7m/s - 21.6 negative sign means opposite direction. = .1m/s in direction of helo flight.
i don't really know.
Physics is poop
To find the initial speed of the package relative to the ground, we can use vector addition. The horizontal speed component of the package will be the same as the helicopter's speed, while the vertical speed component will be zero since the package is ejected horizontally.
First, let's break down the helicopter's velocity into horizontal and vertical components. The horizontal component of the helicopter's velocity is equal to its speed: 21.7 m/s, and the vertical component is zero since the helicopter is flying at a constant altitude with no change in height.
Next, we need to consider the package's velocity relative to the helicopter. It is given that the package is ejected horizontally with an initial speed of 21.6 m/s, opposite to the helicopter's motion. Therefore, the horizontal component of the package's velocity relative to the helicopter will be -21.6 m/s, and the vertical component will be zero.
Now we can find the initial speed of the package relative to the ground by adding the velocities of the helicopter and the package together. Since the horizontal components of both velocities are in the same direction (opposite direction terms will cancel out), we can simply add them:
Horizontal component of the package's velocity relative to the ground = Horizontal component of helicopter's velocity + Horizontal component of package's velocity relative to the helicopter
= 21.7 m/s - 21.6 m/s
Once you find the horizontal component of the package's velocity relative to the ground, you can use the Pythagorean theorem to calculate the magnitude of the package's velocity relative to the ground:
Magnitude of the package's velocity relative to the ground = √((horizontal component of velocity relative to the ground)^2 + (vertical component of velocity relative to the ground)^2)
In this case, the vertical component of the velocity relative to the ground is zero, so the magnitude of the package's velocity relative to the ground will be equal to the horizontal component.