If the helicopter is flying at constant velocity then where will it be when the packet strikes the ground.

Answer

To solve the problem of determining the position of the helicopter when the packet strikes the ground, we can follow these steps:

### Step 1: Understand the Initial Conditions
The helicopter is flying at a constant horizontal velocity \( v \). When the packet is dropped from the helicopter, it initially has the same horizontal velocity \( v \) as the helicopter.

**Hint:** Identify the initial velocities of both the helicopter and the packet.

### Step 2: Analyze the Motion of the Packet
Once the packet is released, it will begin to fall under the influence of gravity. However, it retains its initial horizontal velocity \( v \). Therefore, the packet will follow a parabolic trajectory, moving downward while also moving horizontally.

**Hint:** Remember that the packet's horizontal motion continues at the same velocity while it falls.

### Step 3: Determine the Time of Flight
To find out where the helicopter will be when the packet strikes the ground, we need to calculate the time it takes for the packet to hit the ground. This time can be determined using the formula for free fall:
\[ h = \frac{1}{2} g t^2 \]
where \( h \) is the height from which the packet is dropped, \( g \) is the acceleration due to gravity, and \( t \) is the time of flight.

**Hint:** Use the height of the helicopter to calculate the time it takes for the packet to fall.

### Step 4: Calculate the Horizontal Distance Traveled by the Packet
During the time \( t \) that the packet is falling, it will also travel horizontally. The horizontal distance \( d \) traveled by the packet can be calculated using:
\[ d = v \cdot t \]
where \( v \) is the constant horizontal velocity of the helicopter (and the packet).

**Hint:** Use the time calculated in the previous step to find the horizontal distance.

### Step 5: Determine the Position of the Helicopter
Since the helicopter is flying at a constant horizontal velocity, it will also have traveled the same horizontal distance \( d \) in the same time \( t \). Therefore, when the packet strikes the ground, the helicopter will be at the same horizontal position as the packet.

**Hint:** Remember that both the helicopter and the packet maintain the same horizontal velocity.

### Final Conclusion
When the packet strikes the ground, the helicopter will be directly vertically above the point where the packet lands.

**Final Answer:** The helicopter will be vertically above the packet when it strikes the ground.