A helicopter above the ground is descending at 3.5 m/s. It drops a package from rest(relative to the helicopter). Just before it hits the ground the package is falling at a rate of 13.4 m/s relative to the ground. Find the velocity of the package relative to the helicopter.
9.9 m/s, up
9.9 m/s, down
16.9 m/s, down
16.9 m/s, up
CAN YOU EXPLAIN WHAT TO DO AND THE CORRECT ANSWER? Thanks!
It is falling 13.4 faster than the helicopter is falling
v + 3.5 down = 13.4 down
so
v = 9.9 down
To solve this problem, we need to consider the relative velocities and apply the principles of motion.
First, let's determine the velocity of the package when it was dropped from the helicopter relative to the ground. We know that the helicopter was descending at a rate of 3.5 m/s, and the package was initially at rest relative to the helicopter.
Thus, the initial velocity of the package relative to the ground is the sum of the helicopter's descent velocity and the package's initial velocity (0 m/s):
Velocity of package relative to ground = Velocity of helicopter + Velocity of package
Velocity of package relative to ground = -3.5 m/s + 0 m/s = -3.5 m/s (negative sign indicates downward direction)
Next, we are given that just before it hits the ground, the package is falling at a velocity of 13.4 m/s relative to the ground. The velocity of the package relative to the helicopter at that moment is what we need to find.
Since the helicopter is still descending at 3.5 m/s, the velocity of the package relative to the helicopter is the difference between the package's velocity relative to the ground and the helicopter's velocity:
Velocity of package relative to helicopter = Velocity of package relative to ground - Velocity of helicopter
Velocity of package relative to helicopter = 13.4 m/s - (-3.5 m/s) = 13.4 m/s + 3.5 m/s = 16.9 m/s
Therefore, the correct answer is:
16.9 m/s, up
To solve this problem, we can use the concept of relative velocity. Relative velocity is the velocity of one object as observed from the perspective of another object.
Let's assume the velocity of the package relative to the helicopter is v.
Given information:
- The helicopter is descending at a velocity of 3.5 m/s.
- The velocity of the package relative to the ground just before it hits the ground is 13.4 m/s.
To find the velocity of the package relative to the helicopter, we need to consider the velocities of both the helicopter and the package in the same direction. Since the helicopter is descending, we will consider positive velocities as downward and negative velocities as upward.
Since the velocity of the package relative to the helicopter is in the opposite direction to the helicopter's descent, we can set up the following equation:
v + 3.5 m/s = -13.4 m/s
Now we can solve for v:
v = -13.4 m/s - 3.5 m/s
v = -16.9 m/s
Therefore, the velocity of the package relative to the helicopter is 16.9 m/s, but in the upward direction because the package is dropping relative to the helicopter. Hence, the correct answer is 16.9 m/s, up.