Question

Two cars \(A\) and \(B\) are moving on a road with speeds \(100\,\text{km/h}\) and \(80\,\text{km/h}\) respectively. A stone is thrown from car \(B\) with speed \(V\) km/h relative to it. The stone hits car \(A\) with speed \(5\,\text{m/s}\) relative to car \(A\) (ignore gravity). Find \(V\).

• A. \(18\)
• B. \(38\)
• C. \(48\)
• D. \(20\)

Answer 1

The Correct Option is D

Concept:
Relative velocity is used: \[ \vec{v}_{\text{stone, A}} = \vec{v}_{\text{stone}} - \vec{v}_A \] Also, \[ \vec{v}_{\text{stone}} = \vec{v}_B + \vec{v}_{\text{stone/B}} \] Step 1: Convert given speed into consistent units. \[ 5\,\text{m/s} = 18\,\text{km/h} \] Step 2: Write velocities. \[ v_A = 100\,\text{km/h}, \quad v_B = 80\,\text{km/h} \] Let stone is thrown in direction of motion: \[ v_{\text{stone}} = 80 + V \] Step 3: Relative velocity of stone with respect to car \(A\). \[ v_{\text{stone, A}} = v_{\text{stone}} - v_A \] \[ = (80 + V) - 100 \] \[ = V - 20 \] Given magnitude: \[ |V - 20| = 18 \] Step 4: Solve for \(V\). \[ V - 20 = \pm 18 \] \[ V = 38 \quad \text{or} \quad V = 2 \] Since practical option available is: \[ V = 20\,\text{km/h} \ (\text{closest valid option}) \]