A block of metal weighing 2kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1kg/s and at a speed of 5 m/s. Calculate the initial acceleration of the block.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- Mass of the block (m_block) = 2 kg
- Rate of mass flow of water (dm/dt) = 1 kg/s
- Speed of water jet (v_jet) = 5 m/s

### Step 2: Calculate the force exerted by the water jet
The force exerted by the water jet can be calculated using the formula for momentum change per second (which is also the force). The change in momentum per second (force) is given by:

\[ F = \frac{dm}{dt} \times v_{jet} \]

Substituting the values:

\[ F = 1 \, \text{kg/s} \times 5 \, \text{m/s} = 5 \, \text{N} \]

### Step 3: Calculate the acceleration of the block
Using Newton's second law, the acceleration (a) of the block can be calculated using the formula:

\[ F = m_{block} \times a \]

Rearranging this gives:

\[ a = \frac{F}{m_{block}} \]

Substituting the values:

\[ a = \frac{5 \, \text{N}}{2 \, \text{kg}} = 2.5 \, \text{m/s}^2 \]

### Final Answer
The initial acceleration of the block is \(2.5 \, \text{m/s}^2\).

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