posted by Kacy on .
A suspension bridge is 66.0 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?
(b) If you throw the stone straight down with a speed of 22.5 m/s, how long before it hits the ground?
(c) If you throw the stone with a velocity of 22.5 m/s at 25.0° above the horizontal, how far from the point directly below the bridge will it hit the level ground?
do u go to wayne state?
a. d = 0.5gt^2,
66 = 0.5 * 9.83 t^2,
66 = 4.915t^2,
t^2 = 66 / 4.915 = 13.4,
t = sqrt(13.4) = 3.66 s.
b. d = Vo*t + 0.5gt^2,
66 = 22.5t + 0.5 * 9.83t^2,
66 = 22.5t + 4.915t^2,
4.915t^2 + 22.5t - 66 = 0,
Use Quadratic Formula to find t:
t = (- 22.5+- sqrt(506.25 + 1297.56))/
t = (-22.5 +- 42.47) / 9.83,
t = 2.03 or -6.61, select positive t:
t = 2.03 s.
c. y = Ver.=22.5 m/s * sin25 = 9.5m/s
d(up) = d(down),
Vo*t = 0.5gt^2,
9.5t = 0.5 * 9.83t^2,
9.5t = 4.915t^2
4.915t^2 - 9.5t = 0,
Factor out t:
t(4.915t - 9.5) = 0,
t = 0: 4.915t - 9.5 = 0, 4.915t = 9.5,
t = 1.93 s (Ver),
d = Ver. = 9.5 m/s * 1.93 s = 18.4 m,
d = R = 18.4 m /sin25 = 43.5 m,
d = Hor. = 43.5 m * cos25 = 39.5 m = distance stone lands.