Could you answer the extra credit

2. On watching The Dark Knight (2008) again, I was struck with inspiration for a physics problem. SPOILER ALERT!! In their final confrontation, Batman throws the Joker off of a high building. Half-way down to the ground Batman launches his grapple gun and barely manages to hook Joker and prevent him from hitting the ground. If the building were 500 meters tall, how fast would the grapple gun need to be fired in order to catch the Joker before he hits the ground, assuming Batman waits until the Joker is half-way down to fire? As usual, ignore air resistance. Time taken by the Joker to hit the ground 5 = ut + 2 at 2 500 = 0+ + g+ 2 t = 2(500) = 10.15 9.8 Time elapsed joker at mid way thaif : 2half 2/250) 9 8 Time available for grapple ta= t - thalf = 10.1 - 7.14 = 2.96 sec By using S = ut + at 2 500 = Utg + 1 ( - 9 ) tah 500 = 4( 2.96) - 9.8 ( 2.96 ) U= - 164 m/s 4 = 164 m/s in downward direction EXTRA CREDIT: How fast was Joker moving just prior to being bat-grappled