A suspension bridge is 50.0 m above the level base of a gorge. A stone is thrown

Question

A suspension bridge is 50.0 m above the level base of a gorge. A stone is thrown or dropped from the bridge. At the location of the bridge, g has been measured to be 9.83 m/s2. In each of the following, assume that there is no air resistance.
(a) If you drop the stone, how long does it take for it to fall to the base of the gorge?
s
(b) If you throw the stone straight down with a speed of 21.5 m/s, how long before it hits the ground?
s
(c) If you throw the stone with a velocity of 21.5 m/s at 30.0° above the horizontal, how far from the point directly below the bridge will it hit the level ground?
m

Explanation / Answer

Given Height of the bridge, h = 50 m a)If a stone is dropped , the time taken to reach the base is 50 = 1/2 gt^2    50 = 0.5 *9.83 m/s^2 * t^2 t =3.18 s ------------------------------------------------------------------------------- b) Initial velocity, vi = 21.5 m/s 50 =( 21.5 m/s)t+1/2 (9.83 m/s^2)t^2 4.9t^2+21.5 t-50 =0 t =1.68 s is the time taken to reach the base -------------------------------------------------------------------------------- c)Initial velocity, vi = 21.5 m/s       ? = 300 Horizontal distance, x = vi cos30 *t                                   = 21.5 *0.866 *1.68                                   = 31.28 m Horizontal distance, x = vi cos30 *t                                   = 21.5 *0.866 *1.68                                   = 31.28 m

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