a)the height of the upper falls at Yellowstone nationalpark is 33.2m. when the w

Question

a)the height of the upper falls at Yellowstone nationalpark is 33.2m. when the water reaches the bottom of the falls, itsspeed is 25.8m/s. neglecting air resistance, what isthe speed of the water at the top of the falls
b) batman, mass=91 kg, jumps straight down from a bridge intoa boat , mass=510 kg, in which a criminal is fleeing. the velocityof the boat is initially +11m/s. what is the velocity of the boatafter batman lands on it?
b) batman, mass=91 kg, jumps straight down from a bridge intoa boat , mass=510 kg, in which a criminal is fleeing. the velocityof the boat is initially +11m/s. what is the velocity of the boatafter batman lands on it?

Explanation / Answer

(a) Taking the bottom of the falls to have zero potential energy, asmall mass m of water would have initial kinetic + potential energy(h = 33.2m): (1/2)mv12 + mgh and final kinetic energy only: (1/2)mv22 Since energy is conserved: (1/2)mv12 + mgh = (1/2)mv22 Canceling m and multiplying by 2: v12 + 2gh = v22 Then v12 = v22 -2 gh =(25.8m/s)2 - 2(9.8 m/s2)(33.2 m) = 14.92 v1 = [14.92] = 3.86 m/s

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