A jet is releasing water at the rate of 6 kg/see with speed of 4 m/sec. Now this water strikes a block of mass 10 kg. find the force exerted on block & its acceleration ?

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given data
- The rate of water being released (dm/dt) = 6 kg/s
- The speed of the water (v) = 4 m/s
- The mass of the block (M) = 10 kg

### Step 2: Calculate the thrust force exerted on the block
The thrust force (F) exerted by the jet of water can be calculated using the formula:
\[ F = v \times \frac{dm}{dt} \]
Where:
- \( v \) is the speed of the water
- \( \frac{dm}{dt} \) is the rate of change of mass (mass flow rate)

Substituting the values:
\[ F = 4 \, \text{m/s} \times 6 \, \text{kg/s} \]
\[ F = 24 \, \text{N} \]

### Step 3: Calculate the acceleration of the block
Using Newton's second law of motion, the acceleration (a) of the block can be calculated using the formula:
\[ F = M \times a \]
Rearranging the formula gives:
\[ a = \frac{F}{M} \]

Substituting the values:
\[ a = \frac{24 \, \text{N}}{10 \, \text{kg}} \]
\[ a = 2.4 \, \text{m/s}^2 \]

### Final Answers
- The force exerted on the block is **24 N**.
- The acceleration of the block is **2.4 m/s²**.

---