Asuspension bridge is 60.0 m above the level base of a gorge. a stone is thrown or dropped from the bridge. ignore air resistance. at the location of the bridge g has been measured to be 9.83 m/s2. (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 20.0 m/s, how long before it hits the ground? (c) if you throw the stone with a velocity of 20.0 m/s at 30.0° above the horizontal, how far from the point directly below the bridge will it hit the level ground?

a)

b)

c)Xmax=80.71m

Explanation:

a)Kinematics equation for the Stone, dropped:

      initial position is bridge height

      the stone is dropped

The ball reaches the ground, y=0, at t=t1:

b)Kinematics equation for the Stone, with a initial speed of 20m/s:

      initial position is bridge height

      the stone is thrown straight down

The ball reaches the ground, y=0, at t=t1:

t2=-6.01       this solution does not have physical sense

t2=2.00

c)Kinematics equation for the Stone, with a initial speed of 20m/s with an angle of 30° above the horizontal:

      initial position is bridge height

      the stone is thrown with an angle of 30° above the horizontal

The ball reaches the ground, y=0, at t=t3:

t3=-2.62       this solution does not have physical sense

t3=4.66

the movement in x:

v=constant=20cos(30)m/s

x(t)=v*t

Xmax=v*t3=20cos(30)*4.66=80.71m

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s