Answer:
[tex]h_{B} = 5.012\, m[/tex]
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:
[tex]K_{A} = K_{B} + U_{B}[/tex]
[tex]\frac{1}{2} \cdot m \cdot v_{A}^{2} = \frac{1}{2} \cdot m \cdot v_{B}^{2} + m \cdot g \cdot h_{B}[/tex]
The previous expression is simplified and required height is found:
[tex]h_{B} = \frac{1}{2\cdot g} \cdot (v_{A}^{2}-v_{B}^{2})[/tex]
[tex]h_{B} = \frac{1}{2 \cdot (9.807\, \frac{m}{s^{2}} )} \cdot [(10\, \frac{m}{s} )^{2}-(1.3\, \frac{m}{s} )^{2}][/tex]
[tex]h_{B} = 5.012\, m[/tex]
