Practice question

Given: A hot air balloon ascends at 4 m/s for 6 s, then accelerates at 1.5 m/s² for 4 s . A stone is dropped at this instant. How long does it take to reach the ground if the initial height was 30 m ? (Take g = 10 m/s² ) These values define the system as per NCERT data. Formula: Phase 1: h_1 = 4 · 6 = 24 m. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Phase 2: v = 4 + 1.5 · 4 = 10 m/s, h_2 = 4 · 4 + 1/2 · 1.5 · (4)² = 16 + 12 = 28 m . Total height = 30 + 24 + 28 = 82 m, stone’s initial velocity = 10 m/s upward. -82 = 10 t - 5 t² Rightarrow 5 t² - 10 t - 82 = 0 . Solve: t = frac10 pm sqrt100 + 164010 = 10 pm 41.23/10, t = 5.12 s (positive root). 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.