5. A72 kg pole -vaulter running at 8.4m/s completes a vault. If all of her kinetic energy is transformed into potential energy, what is the maximum height of her vault?

Here's how to solve this problem:<br /><br />**1. Understand the principle:**<br /><br />The problem states that all kinetic energy is converted into potential energy. This means we can use the following equation:<br /><br />Kinetic Energy (KE) = Potential Energy (PE)<br /><br />**2. Write down the formulas:**<br /><br />* KE = (1/2) * m * v² , where m is mass and v is velocity<br />* PE = m * g * h, where m is mass, g is acceleration due to gravity (approximately 9.8 m/s²), and h is height.<br /><br />**3. Set up the equation:**<br /><br />(1/2) * m * v² = m * g * h<br /><br />**4. Solve for height (h):**<br /><br />Notice that the mass (m) appears on both sides of the equation, so we can cancel it out:<br /><br />(1/2) * v² = g * h<br /><br />Now, isolate h:<br /><br />h = (v²) / (2 * g)<br /><br />**5. Plug in the values:**<br /><br />h = (8.4 m/s)² / (2 * 9.8 m/s²)<br /><br />**6. Calculate:**<br /><br />h = 70.56 m²/s² / 19.6 m/s²<br /><br />h ≈ 3.6 m<br /><br />**Answer:** The maximum height of her vault is approximately 3.6 meters.<br />