Question

You and your friends find a rope that hangs down 19m from a high tree branch right at the edge of a river. You find that you can run, grab the rope, swing out over the river, and drop into the water. You run at 2.0 m/s and grab the rope, launching yourself out over the river.How long must you hang on if you want to drop into the water at the greatest possible distance from the edge?

Answer 1

Answer:

Explanation:

Given

length of rope $L=19\ m$

velocity while running $v=2\ m/s$

when the person jumps off the bank and hang on the rope then we can treat the person as pendulum with Time period T which is given by

$T=2\pi \sqrt{\frac{L}{g}}$

$T=2\pi \sqrt{\frac{19}{9.8}}$

$T=2\pi \times 1.392$

$T=8.74\ m/s$

Greatest Possible distance will be covered when person reaches the other extreme end  of assumed pendulum (velocity=zero)

therefore he must hang on for 0.5 T time

$time=0.5\times 8.74=4.37\ s$