Well, those are good ones. Now how about a <u><em>thermometer</em></u> to <em>measure the temperature</em> ?
Answer:
The velocity when the ball hits the ground is obtained using v2. 2 = v1. 2 + 2 g Dy with v1=0 and Dy=h. Thus solving for v2 yields 17.1 m/s v2 = 2 g h =.
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The answer to your question is 343 m/s
Jane's mechanical energy at any time is

where

is the potential energy, while

is the kinetic energy.
Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:

Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:

But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:

from which we can find h, the maximum height Jane can reach: