JEE Mains · Physics · STD 11 - Motion in straight line
- JEE Mains 2026
- Medium
- MCQ
Two cars \(A\) and \(B\) are moving in the same direction along a straight line with speeds \(100\) km/h and \(80\) km/h, respectively such that car \(A\) is moving ahead of car \(B\). A person in car \(B\) throws a stone with a speed \(v\) so that it hits the car \(A\) with a speed of \(5\) m/s. The value of \(v\) is ______ km/h.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(38\)
Step-by-step Solution
Detailed explanation
Velocity of car A, \(v_A = 100\) km/h
Velocity of car B, \(v_B = 80\) km/h
Velocity of the stone relative to car B is \(v\). The velocity of the stone relative to the ground is \(v_S = v_B + v = 80 + v\).
The velocity of the stone relative to car A is \(v_{S/A} = v_S - v_A = (80 + v) - 100 = v - 20\).
The stone hits car A with a relative speed of \(5\) m/s. Converting this speed to km/h:
\(v_{S/A} = 5 \times \dfrac{18}{5} = 18\) km/h
Equating the relative speeds:
\(v - 20 = 18 \Rightarrow v = 38\) km/h
Answer: \(38\)
Velocity of car B, \(v_B = 80\) km/h
Velocity of the stone relative to car B is \(v\). The velocity of the stone relative to the ground is \(v_S = v_B + v = 80 + v\).
The velocity of the stone relative to car A is \(v_{S/A} = v_S - v_A = (80 + v) - 100 = v - 20\).
The stone hits car A with a relative speed of \(5\) m/s. Converting this speed to km/h:
\(v_{S/A} = 5 \times \dfrac{18}{5} = 18\) km/h
Equating the relative speeds:
\(v - 20 = 18 \Rightarrow v = 38\) km/h
Answer: \(38\)
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