An artificial satellite of the earth releases a packet. If air resistance is neglected, the point where the packet will hit, will be

Options

A. ahead
B. exactly below
C. behind
D. it will neaver reach the earth

Answer

To solve the problem, we need to analyze the motion of the packet released from the artificial satellite. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Situation
An artificial satellite is orbiting the Earth at a certain altitude. When the satellite releases a packet, we need to determine the motion of that packet after it is released.

**Hint:** Consider the forces acting on the satellite and the packet when it is released.

### Step 2: Identify the Forces
While the satellite is in orbit, it is subject to gravitational force pulling it towards the Earth, which is balanced by the centripetal force required for circular motion. The gravitational force (Fg) acting on the satellite is given by:

\[ F_g = \frac{GMm}{r^2} \]

where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, \( m \) is the mass of the satellite, and \( r \) is the distance from the center of the Earth to the satellite.

**Hint:** Remember that the packet will experience the same gravitational force as the satellite at the moment of release.

### Step 3: Analyze the Packet's Initial Conditions
When the packet is released, it retains the same horizontal velocity (v) as the satellite. This means that it has both a downward gravitational acceleration and a horizontal velocity.

**Hint:** Think about how the packet's motion will change after it is released.

### Step 4: Determine the Motion of the Packet
Once released, the packet will begin to fall towards the Earth due to gravity. However, it will also continue to move horizontally at the same speed as the satellite. This creates a curved trajectory.

**Hint:** Consider the concept of projectile motion and how the packet will follow a parabolic path.

### Step 5: Conclusion on the Packet's Path
Since the packet has a horizontal velocity and is also falling towards the Earth, it will not fall straight down. Instead, it will continue to move forward while falling, effectively following a trajectory that matches the curvature of the Earth.

However, because it retains the orbital velocity, it will not hit the Earth; instead, it will continue to orbit the Earth indefinitely.

**Final Answer:** The packet will never reach the Earth.

### Summary of Steps:
1. Understand the situation of the satellite and packet.
2. Identify the forces acting on the satellite and packet.
3. Analyze the initial conditions of the packet upon release.
4. Determine the motion of the packet after release.
5. Conclude that the packet will never hit the Earth.