The specialty of an athlete on the women's track team is the pole vault. She has a mass of 48 kg and her approach speed is 8.9 m/s. When she is directly above the bar, her speed is 1.6 m/s. Neglecting air resistance and any energy absorbed by the pole, determine the amount (in m) she has raised herself as she crosses the bar.

H = 3.9 m

Explanation:

mass (m) = 48 kg

initial velocity (initial speed) (U) = 8.9 m/s

final velocity (V) = 1.6 m/s

acceleration due to gravity (g) = 9.8 m/s^{2}

find the height she raised her self to as she crosses the bar (H)

from energy conservation, the change in kinetic energy = change in potential energy

0.5m (V^{2} - [test]U^{2}[/tex]) = mg (H-h)

where h = initial height = 0 since she was on the ground

the equation becomes

0.5m (V^{2} - [test]U^{2}[/tex]) = mgH

0.5 x 48 x (1.6^{2} - [test]8.9^{2}[/tex]) = 48 x 9.8 x H

-1839.6 = 470.4 H (the negative sign indicates a decrease in kinetic energy so we would not be making use of it further)

H = 3.9 m