\ \ \ \ \ \ \ \

Jane running along the level ground with a velocity of 5.6 m/s. She has kinetic energy, but nothing else.

After: Jane having swung up to some height h, and momentarily at rest. Here she has potential energy, and nothing else.

Initially Jane is running along the ground with a velocty is 4.9 m/sec.

Kinetic Energy : $\"\"$ .

After that Jane swung up to some height h and come into rest.

Potential Energy : $\"\"$ .

From the law of conservation of energy, $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$

$\"\"$

Therefore, Jane can swing 1.225 m high.

(b)

From part (a): The Jane swings to a height $\"\"$ .

The height does not depends on the length of the vine or the rope.

Longer the vine, the smaller will be the angle required for Jane to swing to reach a particular height.

No, the height does not depends on the length of the vine.