truck is moving with a speed of 15 m/s. A car chasing this truck with a speed of 10 m/s fires a bullet at truck with muzzle velocity 90 km/h. The speed with which the bullet hit the truck is

Options

A. 15 m/s
B. 20 m/s
C. 25 m/s
D. 30 m/s

Answer

To solve the problem, we need to find the speed at which the bullet hits the truck. We will follow these steps:

### Step 1: Convert the muzzle velocity of the bullet from km/h to m/s
The muzzle velocity is given as 90 km/h. We can convert this to meters per second using the conversion factor:

\[ \text{Velocity in m/s} = \text{Velocity in km/h} \times \frac{5}{18} \]

Calculating this gives:

\[ 90 \, \text{km/h} \times \frac{5}{18} = 25 \, \text{m/s} \]

### Step 2: Determine the speed of the bullet relative to the ground
The car is moving at a speed of 10 m/s, and it fires the bullet in the same direction. Therefore, the speed of the bullet relative to the ground is the sum of the bullet's muzzle velocity and the speed of the car:

\[ \text{Bullet speed relative to ground} = \text{Muzzle velocity} + \text{Car speed} \]

Substituting the values:

\[ \text{Bullet speed relative to ground} = 25 \, \text{m/s} + 10 \, \text{m/s} = 35 \, \text{m/s} \]

### Step 3: Determine the speed of the truck relative to the ground
The truck is moving at a speed of 15 m/s.

### Step 4: Calculate the relative speed of the bullet with respect to the truck
Since both the bullet and the truck are moving in the same direction, the speed of the bullet as observed from the truck is the difference between the bullet's speed relative to the ground and the truck's speed:

\[ \text{Relative speed of bullet with respect to truck} = \text{Bullet speed relative to ground} - \text{Truck speed} \]

Substituting the values:

\[ \text{Relative speed of bullet with respect to truck} = 35 \, \text{m/s} - 15 \, \text{m/s} = 20 \, \text{m/s} \]

### Final Answer
The speed with which the bullet hits the truck is **20 m/s**.

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