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

`h_(B) = 5.012\, m`

Step-by-step 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)`

`(1)/(2) \cdot m \cdot v_(A)^(2) = (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) = (1)/(2\cdot g) \cdot (v_(A)^(2)-v_(B)^(2))`

`h_(B) = (1)/(2 \cdot (9.807\, (m)/(s^(2)) )) \cdot [(10\, (m)/(s) )^(2)-(1.3\, (m)/(s) )^(2)]`

`h_(B) = 5.012\, m`