Question

The specialty of an athlete on the women's track team is the pole vault. She has a mass of 60.0 kg and her approach speed is 9.20 m/s. When she is directly above the bar, her speed is 2.40 m/s. Neglecting air resistance and any energy absorbed by the pole, determine the amount she has raised herself as she crosses the bar.

Answer 1

She raised approximately 4 meters as she crosses the bar

Step-by-step explanation:

Energy Conservation

In the absence of air resistance and any other energy-absorbing events, the total mechanical energy is conserved. Recall the mechanical energy is the sum of the gravitational potential energy and the kinetic energy:

`\displaystyle M=m.g.h+(1)/(2)m.v^2`

When our athlete is at the ground level her height is 0, thus she has only kinetic energy given by the speed she's at when starting the jump:

`\displaystyle M_1=m.g.(0)+(1)/(2)m.v^2=(1)/(2)m.v^2`

Later when she's directly above the bar, she has both energies since some speed remains at a certain height h we must calculate. The mechanical energy is

`\displaystyle M_2=m.g.h+(1)/(2)m.v'^2`

Equating both energies

`\displaystyle m.g.h+(1)/(2)m.v'^2=(1)/(2)m.v^2`

Simplifying by m and rearranging

`\displaystyle m.g.h=(1)/(2)m.v^2-(1)/(2)m.v'^2=(1)/(2)(v^2-v'^2)`

Solving for h

`\displaystyle h=((v^2-v'^2))/(2g)=((9.2^2-2.4^2))/(2\cdot 9.8)`

`\boxed{h=4.02\ m}`

She raised approximately 4 meters as she crosses the bar