Determine the initial velocity (u) of the stone.

Step 1: Determine the initial velocity (u) of the stone. We use the kinematic equation for displacement: s = ut + (1)/(2)at^2. Let the upward direction be positive. The initial position is 85 m above the ground. The final position is 0 m (ground level). So, the displacement s = 0 - 85 = -85 m. The acceleration due to gravity a = -g = -9.8 m/s^2. The total time t = 5 s. s = ut + (1)/(2)at^2 -85 = u(5) + (1)/(2)(-9.8)(5)^2 -85 = 5u - 4.9(25) -85 = 5u - 122.5 5u = 122.5 - 85 5u = 37.5 u = (37.5)/(5) u = 7.5 m/s Step 2: Calculate the greatest height above the ground (i). The stone reaches its maximum height when its vertical velocity becomes 0 m/s. We use the kinematic equation: v^2 = u^2 + 2as. Here, v = 0 m/s, u = 7.5 m/s, and a = -9.8 m/s^2. Let h_add be the additional height reached above the tower. 0^2 = (7.5)^2 + 2(-9.8)h_add 0 = 56.25 - 19.6 h_add 19.6 h_add = 56.25 h_add = (56.25)/(19.6) h_add ≈ 2.87 m The greatest height above the ground is the tower's height plus this additional height. H_ground = 85 m + 2.87 m H_ground = 87.87 m The greatest height above the ground is 87.87 m. Step 3: Calculate the velocity with which it reaches the ground (ii). We use the kinematic equation: v = u + at. Here, u = 7.5 m/s, a = -9.8 m/s^2, and t = 5 s. v = 7.5 + (-9.8)(5) v = 7.5 - 49 v = -41.5 m/s The negative sign indicates the velocity is directed downwards. The velocity with which it reaches the ground is 41.5 m/s downwards. Step 4: Calculate the time taken to reach the maximum height (iii). We use the kinematic equation: v = u + at. At maximum height, the final velocity v = 0 m/s. Here, u = 7.5 m/s and a = -9.8 m/s^2. 0 = 7.5 + (-9.8)t_max 9.8 t_max = 7.5 t_max = (7.5)/(9.8) t_max ≈ 0.77 s The time taken to reach the maximum height is 0.77 s. Send me the next one 📸