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1. A stone is thrown horizontally with an initial speed of 10m/s from a bridge. If air resistance could be ignored, how long would it take the stone to strike the water 80m below the bridge?2. A stone is thrown horizontally with an initial speed of 30m/s from a bridge. Find the stone's total speed when... 顯示更多 1. A stone is thrown horizontally with an initial speed of 10m/s from a bridge. If air resistance could be ignored, how long would it take the stone to strike the water 80m below the bridge? 2. A stone is thrown horizontally with an initial speed of 30m/s from a bridge. Find the stone's total speed when it enters the water 4s later. 更新: 3. A soccer ball, at rest on the ground, is kicked with an initial velocity of 10m/s at a launch of 30 degrees. Calculate its total flight time, assuming that air resistance is negligible.

最佳解答:

1. Take the downward direction be positive. Displacement, s = 80 m Acceleration due to gravity, a = 10 m/s2 Initial speed, u = -10 m/s So, by the equation, s = ut + 1/2 at2 80 = (-10)t + 1/2 (10)t2 t2 - 2t - 16 = 0 t = 5.12 s or -3.12 (rejected) So, it takes 5.12 s for the stone to strike the water 80 m below. 2. Assume the vertical speed of the stone is uniform when entered in water. By the equation, v2 = u2 + 2as v2 = (-10)2 + 2(10)(80) v2 = 1700 v = 41.23 m/s So, the vertical speed of the stone is 41.23 m/s when entered into water. 圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/1.jpg?t=1182579681 So, total speed = √(vertical speed2 + horizontal speed2) total speed = √(41.232 + 302) total speed = √(1700 + 900) total speed = 51.0 m/s 3. 圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/11.jpg?t=1182579728 The velocity can be resolved into two components. For the vertical speed, v = 10sin30° v = 5 m/s Assume the upward direction to be positive. So, displacement, s = 0 initial speed, u = 5 m/s Accleration due to gravity, a = -10 m/s2 So, by the equation, s = ut + 1/2 at2 0 = (5)t + 1/2 (-10)t2 t2 - t = 0 t(t - 1) = 0 t = 1 s or 0 (rejected) So, the total flight time is 1 s.

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