A suspension bridge is 54.0 m above the level base of a gorge. A stone is thrown

Question

A suspension bridge is 54.0 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 15.5 m/s, how long before it hits the ground? s (c) If you throw the stone with a velocity of 15.5 m/s at 25.0

Explanation / Answer

a)
Using the general equation: Y = Yo + Voy t - (1/2)gt^2
Substituting: 0 = 54.0 + 0 - (0.5)(9.83)t^2
t = 3.315 seconds

b)
Substituting: 0 = 54.0 + (-15.0)t - (0.5)(9.83)t^2

Rearranging: 4.915 t^2 + 15.0 t - 54.0 = 0

Solve for t using quadratic fomula
t = [-15.0 +/- sqrt(1286.64)] / 9.83 <======= Ignore negative root as it is meaningless
t = 2.123 seconds

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