A helicopter 8.40 m above the ground and descending at 4.50 m/s drops a package from rest (relative to the helicopter). We have chosen the positive positive direction to be upward. The package falls freely.
a. Just as it hits the ground, find the y -component of the velocity of the package relative to the helicopter.
b. Just as it hits the ground, find the y -component of the velocity of the helicopter relative to the package.
To find the y-component of the velocity of the package relative to the helicopter just as it hits the ground, we can use the concept of relative velocity.
a. The package is dropped from rest relative to the helicopter, so initially, its velocity relative to the helicopter is zero. Since the helicopter is descending at a constant rate, the package will share the same downward velocity as the helicopter.
To find the y-component of the velocity of the package relative to the helicopter, we need to take into account the downward component of the helicopter's velocity. The velocity of the helicopter is downward, so the y-component of its velocity will be negative.
Therefore, the y-component of the velocity of the package relative to the helicopter just as it hits the ground will be the same as the y-component of the helicopter's velocity.
b. To find the y-component of the velocity of the helicopter relative to the package just as it hits the ground, we can use the concept of relative velocity.
Since the package is falling freely, it will have a downward velocity relative to the ground. The helicopter, on the other hand, is descending at a constant rate and also has a downward velocity relative to the ground.
To find the y-component of the velocity of the helicopter relative to the package just as it hits the ground, we subtract the y-component of the package's velocity from the helicopter's velocity.
Since the package's velocity is downward, its y-component will be negative.
Therefore, the y-component of the velocity of the helicopter relative to the package just as it hits the ground will be the same as the y-component of the helicopter's velocity.