Question

A 54 kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.3 m/s. The acceleration of gravity is 9.8 m/s 2 . Find her altitude as she crosses the bar. Neglect air resistance, as well as any energy absorbed by the pole. Answer in units of m

Answer 1

Answer:

$h_{B} = 5.012\, m$

Explanation:

It is assumed that pole vaulter began running at a height of zero. The physical model is formed after the Principle of Energy Conservation:

$K_{A} = K_{B} + U_{B}$

$\frac{1}{2} \cdot m \cdot v_{A}^{2} = \frac{1}{2} \cdot m \cdot v_{B}^{2} + m \cdot g \cdot h_{B}$

The previous expression is simplified and required height is found:

$h_{B} = \frac{1}{2\cdot g} \cdot (v_{A}^{2}-v_{B}^{2})$

$h_{B} = \frac{1}{2 \cdot (9.807\, \frac{m}{s^{2}} )} \cdot [(10\, \frac{m}{s} )^{2}-(1.3\, \frac{m}{s} )^{2}]$

$h_{B} = 5.012\, m$