Bài 2: Có 45 Kg Bột Mì đựng đều Trong 9 - Gauthmath

Step 1: Calculate the vertical component of the initial velocity: Given: Initial speed = 30 m/s, angle = 53° Vertical component of velocity = 30 * sin(53°) = 30 * 0.7986 ≈ 23.96 m/s

Step 2: Calculate the time taken to reach the maximum height: Using the vertical component of velocity, acceleration due to gravity (g = 9.81 m/s^2), and the height of the cliff (100 m): v = u + at, where v = 0 at maximum height 0 = 23.96 - 9.81t t = 23.96 / 9.81 ≈ 2.44 s

Step 3: Calculate the maximum height above the edge of the cliff: Using the time to reach the maximum height and the vertical component of velocity: h = uyt - 0.5 * g * t^2 h = 23.96 * 2.44 - 0.5 * 9.81 * (2.44)^2 h ≈ 29.3 m †Answer: Answer: (a) h = 29.3 m

Step 4: Calculate the horizontal distance traveled when at maximum altitude: Horizontal distance = horizontal component of velocity * time Horizontal component of velocity = 30 * cos(53°) ≈ 18.2 m/s Horizontal distance = 18.2 * 2.44 ≈ 44.43 m †Answer: Answer: (b) x = 44.43 m

Step 5: Calculate the total time of flight: Using the vertical component of velocity and acceleration due to gravity: v = u + at, where v = 0 at the time of hitting the ground 0 = 23.96 - 9.81t t = 23.96 / 9.81 ≈ 2.44 s (time to reach maximum height) Total time of flight = 2.44 * 2 ≈ 4.88 s

Step 6: Calculate the range of the rock: Range = horizontal component of velocity * total time of flight Range = 18.2 * 4.88 ≈ 88.78 m †Answer: Answer: (d) x = 88.78 m

Step 7: Calculate the horizontal and vertical positions of the rock at t = 2.0 s: Horizontal position: Horizontal distance = horizontal component of velocity * time Horizontal distance = 18.2 * 2 = 36.4 m ≈ 36 m Vertical position: Using the vertical component of velocity, time, and acceleration due to gravity: y = uyt - 0.5 * g * t^2 y = 23.96 * 2 - 0.5 * 9.81 * (2)^2 y ≈ 28.4 m †Answer: Answer: (e) y = 28.4 m, x = 36 m