The Joker has set a trap for Batman, using his own son Nemo as bait. The Joker attaches a very heavy bowling ball of mass M= 300kg to a long wire of length =30m, then attaches the other end of the wire to the incredibly vaulted ceiling of his Joker tower so that the bowling ball hangs at rest just above the ground without touching. The Joker then pulls the bowling ball sideways along its arc of constant radius from the ceiling until it touches the side wall, where Joker attaches it with an electromagnet. Joker then puts Nemo in a big plastic bag with water in it and places him on the floor directly beneath the ceiling attachment of the wire, where the bowling ball had been hanging at rest. He then lies in wait for Batman to arrive.

a) Since the wire is so long, the bowling ball attached to the wall is still hanging at a small angle of 0.340.34 radians from its vertical equilibrium point. How far is Nemo away from the wall where the bowling ball is attached (in meters)?

b) Batman is only 0.5 m tall and has flippers that only reach up to the top of her head, but she can jump 1.0 m off the ground. Can Batman reach where the bowling ball has been attached to the wall? (True = Yes, False = No. Explain your answer in your write-up.)

c)The Joker is planning to release the bowling ball from the wall so that it swings down like a pendulum to bash Batman as he is finding a way to save Nemo from the bag of water. How long does Batman have (in seconds) to save Nemo after Joker pushes the release button on the remote? (Hint: What fraction of a pendulum period does the bowling ball have to travel to reach the bottom of its arc? Assume small enough angles for the pendulum to oscillate harmonically.)

d) How fast will the bowling ball be moving (in meters per second) when it reaches the bottom of its arc where Nemo is? (Hint: Think about energy conservation for a simpler solution, though you can also think about torque and angular acceleration.)