# A mass hangs on the end of a massless rope. The pendulum is held horizontal and released from rest. When the mass reaches the bottom of its path it is moving at a speed v = 2.8 m/s and the tension in the rope is T = 21.7 N.

1)Now a peg is placed 4/5 of the way down the pendulum’s path so that when the mass falls to its vertical position it hits and wraps around the peg.
How fast is the mass moving when it is at the same vertical height as the peg (directly to the right of the peg)?
2)Return to the original mass. What is the tension in the string at the same vertical height as the peg (directly to the right of the peg)?

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1. A person throws a stone straight upward at an initial speed of 15 m/s on a bridge that is 25m above the surface of the water. If the stone just misses the bridge on the way down, What is the speed of the stone just before it hits the water?

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2. 26.73 m/s

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3. A small rock is thrown vertically upward with a speed of 17.0m/s from the edge of the roof of a 32.0m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected. What is the speed of the rock just before it hits the street? How much time elapses from when the rock is thrown until it hits the street?

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4. 1)
(1/2)mv^2 = mgh, where h is 4/5 of the height

2)
T=ma, where a = v^2/r, v being answer from part 1 and r is 1/5 of length of rope

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