Range R = u²sin(2θ)/g. sin(2θ) maximum (=1) when 2θ=90° ⇒ θ=45°. Standard result for level ground projection. Memory aid: 'Max range at 45°; max height at 90°'. Projectile motion fact frequently tested in competitive exams.
Explanation:
Sound travels to cliff and back. Total distance = speed × time = 340 × 2 = 680 m. So distance to cliff = 680/2 = 340 m. Use formula d = (v × t)/2. Time for round trip. Minimum distance for echo 17 m (approx) for 0.1 s persistence.
Explanation:
First law of thermodynamics: Energy is conserved in an isolated system. It changes forms (kinetic to potential etc.) but total constant. Perpetual motion machine impossible.
Explanation:
Let distance d, usual time t hours. d/5 = t + 10/60, d/6 = t - 5/60. Subtract: d/5 - d/6 = (15/60) => d/30 = 0.25 => d = 7.5 km. Commonly asked.
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