An object of mass m is thrown vertically upwards. At what rate will its momentum change?

Options

A. `mg`
B. `mg^2`
C. `(1)/(mg^2)`
D. `(1)/(mg)`

Explanation

To determine the rate at which the momentum of an object of mass \( m \) changes when it is thrown vertically upwards, we can follow these steps:

### Step 1: Understand the concept of momentum
Momentum \( p \) is defined as the product of mass and velocity:
\[ p = m \cdot v \]
where \( m \) is the mass of the object and \( v \) is its velocity.

### Step 2: Identify the forces acting on the object
When the object is thrown upwards, the only force acting on it is the gravitational force, which acts downwards. This force can be expressed as:
\[ F = m \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

### Step 3: Apply Newton's second law of motion
According to Newton's second law, the rate of change of momentum is equal to the net force acting on the object:
\[ \frac{dp}{dt} = F \]
Since the only force acting on the object is the gravitational force, we can substitute this into the equation:
\[ \frac{dp}{dt} = m \cdot g \]

### Step 4: Conclusion
Thus, the rate of change of momentum of the object when thrown vertically upwards is:
\[ \frac{dp}{dt} = m \cdot g \]

### Final Answer
The rate at which the momentum changes is \( m \cdot g \).

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