Practice question

Given: Two balls are thrown upwards simultaneously from the ground with speeds 20 m/s and 30 m/s . After how much time do they have the same velocity? (Take g = 10 m/s² ) These values define the system as per NCERT data. Formula: Velocity: v_1 = 20 - 10 t, v_2 = 30 - 10 t. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Set v_1 = v_2 : 20 - 10 t = 30 - 10 t, not possible directly, so consider relative motion or when one overtakes. Correction: They have same velocity magnitude when one is going up and other down. Time to max height: t_1 = 2 s, t_2 = 3 s . After t_2, v_2 = 30 - 10 (t - 3) downward. At t = 5 s : v_1 = 20 - 10 · 5 = -30 m/s, v_2 = 30 - 10 · 2 = 10 m/s (no match). Instead, equal velocity occurs at t = 1 s relative difference: v_1 = 10 m/s, v_2 = 20 m/s (misstep). Correct: Equal magnitude opposite direction after t = 2 s, v_2 = 10 m/s down at t = 4 s, v_1 = -20 m/s . Time = 4 s . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.