Suzy drops a rock from the roof of her house. Mary sees the rock pass her 5.7 m tall window in 0.186 sec. From how high above the top of the window was the rock dropped? The acceleration of gravity is 9.8 m/s2.Answer in units of m
Suzy drops a rock from the roof of her house. Mary sees the rock pass her 5.7 m tall window in 0.186 sec. From how high above the top of the window was the rock dropped? The acceleration of gravity is 9.8 m/s2 vf = vi + a * t = vi + 9.8 * 0.186 Eq#2: vf = vi + 1.8228 Substitute vi + 1.8228 for vf in Eq#1 (vi + 1.8228)^2 – vi^2 = 111.72 vi^2 + 3.6456 * vi + 1.8228^2 – vi^2 = 111.72 3.6456 * vi + 1.8228^2 = 117.72 3.6456 * vi = 111.72 – 1.8228^2 vi = (111.72 – 1.8228^2) ÷ 3.6456 = 29.73 m/s To determine the initial height of the stone, we need to know the distance the stone falls before it reaches the top of the window. Distance = Average velocity * time Average velocity = ? * (vi + vf) Distance = ? * (vi + vf) * time 5.7 = ? * (vi + vf) * 0.186 Eq#1: vi + vf = 5.7 ÷ 0.093 vf = vi + a * t vf = vi + 9.8 * 0.186 Eq#2: vf = vi + 1.8228 Substitute vi + 1.8228 for vf in Eq#1. vi + vi + 1.8228 = 5.7 ÷ 0.093 2 * vi = (5.7 ÷ 0.093) – 1.8228 vi = [(5.7 ÷ 0.093) – 1.8228] ÷ 2 vi = 29.73 m/s This is the velocity of the rock when it reaches the top of the window. As the rock falls from her hand to the top of the window, its velocity increases from 0 m/s to 29.73 m/s at the rate of 9.8 m/s each second. Time of fall = 29.73 ÷ 9.8 Distance of fall = ? * a * t^2 = ? * 9.8 * (29.73 ÷ 9.8)^2 Distance of fall = 45.1 meters This is the distance from Suzy’s hand to the top of the window. Check vf^2 = vi^2 + 2 * a * d, vi = 0 m/s, a = 9.8 m/s^2, d = 45.1 m vf^2 = 2 * 9.8 * 45.1 vf = √(2 * 9.8 * 45.1) = 29.73 m/s This is the velocity at the top of the window. Velocity at the bottom of the window = 29.73 + 9.8 * 0.186 = 31.5528 Distance = ? * (vi + vf) * time = ? * (29.73 + 31.5528) * 0.186 = 5.7 m This is the height of the window. So, I believe the answer is correct.
