Question

Two cars A & B are moving on a road with speed 100 km/hr and 80 km/hr. A stone is thrown from car B with speed \( V \) km/hr relative to it. Stone hits the car A with speed 5 m/s with respect to car A (ignore gravity). The value of \( V \) is: [All given velocities are in the same direction]

• A. 40 km/hr
• B. 38 km/hr
• C. 38 m/s
• D. 40 m/s

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a relative motion problem. The velocity of the stone in the ground frame must be calculated first, and then its relative velocity with respect to car A is determined.

Step 2: Key Formula or Approach:
1. Velocity of stone w.r.t ground: \( v_{s,g} = v_{s,B} + v_{B,g} \). 2. Velocity of stone w.r.t car A: \( v_{s,A} = v_{s,g} - v_{A,g} \).

Step 3: Detailed Explanation:
Given: \( v_{A,g} = 100 \) km/hr, \( v_{B,g} = 80 \) km/hr, \( v_{s,B} = V \). Relative velocity of stone w.r.t A in km/hr: Convert 5 m/s to km/hr: \( 5 \times \frac{18}{5} = 18 \) km/hr. \[ v_{s,g} = V + 80 \] \[ v_{s,A} = (V + 80) - 100 = V - 20 \] We know \( v_{s,A} = 18 \) km/hr: \[ 18 = V - 20 \] \[ V = 38 \, \text{km/hr} \]

Step 4: Final Answer:
The value of \( V \) is 38 km/hr.