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 m//s`
B. `27 m//s`
C. `450 m//s`
D. `250 m//s`

Explanation

To solve the problem, we need to find the velocity of the bullet as it strikes the thief's jeep. We'll break this down step by step.

### Step 1: Convert all velocities to the same unit
First, we need to convert the velocities from km/h to m/s for consistency.

- **Police jeep velocity**:
\[ 45 \text{ km/h} = \frac{45 \times 1000}{3600} = 12.5 \text{ m/s} \]

- **Thief jeep velocity**:
\[ 153 \text{ km/h} = \frac{153 \times 1000}{3600} = 42.5 \text{ m/s} \]

- **Bullet muzzle velocity**:
\[ 180 \text{ m/s} \text{ (already in m/s)} \]

### Step 2: Determine the relative velocity of the bullet with respect to the ground
The bullet's velocity with respect to the ground is the sum of the bullet's muzzle velocity and the velocity of the police jeep (since the bullet is fired from the police jeep).

\[ \text{Velocity of bullet with respect to ground} = \text{Muzzle velocity} + \text{Police jeep velocity} \]
\[ = 180 \text{ m/s} + 12.5 \text{ m/s} = 192.5 \text{ m/s} \]

### Step 3: Determine the velocity of the thief jeep with respect to the ground
The velocity of the thief's jeep is already calculated as 42.5 m/s.

### Step 4: Calculate the velocity of the bullet with respect to the thief's jeep
To find the velocity of the bullet as it strikes the thief's jeep, we subtract the velocity of the thief's jeep from the velocity of the bullet with respect to the ground.

\[ \text{Velocity of bullet with respect to thief} = \text{Velocity of bullet with respect to ground} - \text{Velocity of thief jeep} \]
\[ = 192.5 \text{ m/s} - 42.5 \text{ m/s} = 150 \text{ m/s} \]

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

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