A police jeep is chasing with, velocity of `45 km//h` a thief in another jeep moving with velocity `153 km//h`. Police fires a bullet with muzzle velocity of `180 m//s`. The velocity it will strike the car of the thief is.

Options

A. `150 ms^(-1)`
B. `27 ms^(-1)`
C. `450 ms^(-1)`
D. `250 ms^(-1)`

Explanation

To solve the problem, we need to find the velocity of the bullet with respect to the thief's jeep. Here’s a step-by-step breakdown of the solution:

### Step 1: Convert the velocities from km/h to m/s
The velocities given in the problem are:
- Police jeep velocity (Vp) = 45 km/h
- Thief jeep velocity (Vt) = 153 km/h

To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]

Calculating:
- \( Vp = 45 \times \frac{1000}{3600} = 12.5 \text{ m/s} \)
- \( Vt = 153 \times \frac{1000}{3600} = 42.5 \text{ m/s} \)

### Step 2: Calculate the relative velocity of the thief's jeep with respect to the police jeep
The relative velocity of the thief's jeep with respect to the police jeep (Vtp) can be calculated using:
\[ Vtp = Vt - Vp \]

Substituting the values:
\[ Vtp = 42.5 \text{ m/s} - 12.5 \text{ m/s} = 30 \text{ m/s} \]

### Step 3: Determine the velocity of the bullet with respect to the ground
The muzzle velocity of the bullet (Vb) is given as:
- \( Vb = 180 \text{ m/s} \)

### Step 4: Calculate the velocity of the bullet with respect to the thief's jeep
The velocity of the bullet with respect to the thief's jeep (Vb_t) can be calculated using:
\[ Vb_t = Vb - Vtp \]

Substituting the values:
\[ Vb_t = 180 \text{ m/s} - 30 \text{ m/s} = 150 \text{ m/s} \]

### Conclusion
The velocity at which the bullet will strike the car of the thief is:
\[ \text{Velocity of bullet with respect to thief's jeep} = 150 \text{ m/s} \]

### Final Answer
The bullet will strike the car of the thief at a velocity of **150 m/s**.

---