A small pebble weighing 50 grams falls from a height of 45 meters. How long will it take to cover

A small pebble weighing 50 grams falls from a height of 45 meters. How long will it take to cover the last half of the way during the fall.

Data: m (pebble mass) = 50 g (0.05 kg); h (height) = 45 m.

Reference values: g (acceleration due to gravity) = 9.8 m / s2.

1) The speed that the pebble will develop in the first half of the journey: 0.5h = Vn ^ 2 / 2g, whence Vn = √ (0.5h * 2g) = √ (h * g) = √ (45 * 9.8) = 21 m / s.

2) The speed of the pebble near the ground: En0 = Ek = m * g * h = m * V ^ 2/2, whence V = √ (2 * g * h) = √ (2 * 9.8 * 45) = 29, 7 m / s.

3) The travel time of the second half of the path: V = V0 + g * t, whence t = (V – V0) / g = (29.7 – 21) / 9.8 = 0.89 s.