Differentiate between progressive waves and stationary waves, and solve a physics problem involving a falling child.

You're on a roll — here are the solutions for questions 4 and 5: 4. Differentiate between progressive waves and stationary waves i) Amplitude of vibration of the particles of the medium • In a progressive wave, all particles of the medium vibrate with the same amplitude (assuming no energy loss). • In a stationary wave, the amplitude of vibration varies with position. It is zero at the nodes and maximum at the antinodes. ii) Phase of vibration of the particles of the medium • In a progressive wave, the phase of vibration changes continuously from one particle to the next. Particles at different positions have different phases. • In a stationary wave, all particles between two consecutive nodes vibrate in phase. Particles on opposite sides of a node vibrate out of phase (180° phase difference). 5. A 'supper man' is sitting on a tree... Let H = 98 m be the initial height of the child. Let g = 9.8 m/s^2 be the acceleration due to gravity. Let t be the time in seconds from when the child starts falling. Step 1: Determine the child's motion. The child falls with an initial velocity of u_c = 0 m/s. The distance fallen by the child after time t is d_c = u_c t + (1)/(2)gt^2. d_c = 0 · t + (1)/(2)(9.8)t^2 d_c = 4.9t^2 The height of the child from the ground at time t is h_c = H - d_c. h_c = 98 - 4.9t^2 Step 2: Determine the 'Supper man's' motion. The 'Supper man' starts flying 2 seconds after the child falls. So, the time the 'Supper man' flies is t_SM = t - 2 (for t 2). The 'Supper man' flies at a constant speed of v_SM = 39.2 m/s. The distance covered by the 'Supper man' is d_SM = v_SM · t_SM. d_SM = 39.2(t-2) The height of the 'Supper man' from the ground at time t is h_SM = H - d_SM. h_SM = 98 - 39.2(t-2) Step 3: Calculate the time when the 'Supper man' catches the child. The 'Supper man' catches the child when their heights are equal, i.e., h_c = h_SM. 98 - 4.9t^2 = 98 - 39.2(t-2) 4.9t^2 = 39.2(t-2) 4.9t^2 = 39.2t - 78.4 Rearrange into a quadratic equation: 4.9t^2 - 39.2t + 78.4 = 0 Divide the entire equation by 4.9: (4.9t^2)/(4.9) - (39.2t)/(4.9) + (78.4)/(4.9) = 0 t^2 - 8t + 16 = 0 This is a perfect square trinomial: (t-4)^2 = 0 t = 4 s The 'Supper man' catches the child after 4 seconds from when the child started falling. Step 4: Calculate the height from the ground where the child is caught. Substitute t=4 s into the child's height equation: h_c = 98 - 4.9t^2 h_c = 98 - 4.9(4)^2 h_c = 98 - 4.9(16) h_c = 98 - 78.4 h_c = 19.6 m The child is caught at a height of 19.6 m from the ground. That's the last one for today! Send me the next one 📸