A 80-kg base runner begins his slide into second base when he is moving at a speed of 3.7 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. A 45-kg pole vaulter running at 11 m/s vaults over the bar. Her speed when she is above the bar is 1.1 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

  the vaulter has a height of 6.112 meters

Explanation:

Base runner: no question content.

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Pole vaulter:

Initial kinetic energy* is ...

  KE = (1/2)mv^2 = (1/2)(45 kg)(11 m/s)^2 = 2722.5 J

Above the bar, her kinetic energy is ...

  KE = (1/2)mv^2 = (1/2)(45 kg)(1.1 m/s)^2 = 27.225 J

Then the amount of kinetic energy converted to potential energy is ...

  2722.5 J -27.225 J = 2695.275 J

This corresponds to a change in height of ...

  PE = mgh

  2695.275 J = (45 kg)(9.8 m/s^2)h

  h = 2695.275/(45·9.8) m = 6.112 m

Her altitude above the bar is 6.112 meters.

* Here, we use the traditional equations for kinetic and potential energy, which use "m" to represent mass. When we fill in the numbers, we attach units to the numbers in which "m" represents "meters". We trust you can sort this without confusion.

what are the options.

explanation: