Question

A 78.0 kg pole vaulter runs with a speed of 8.21 m/s. The maximum change in height that they can expect to rise, expressed to three significant digits, is ___________ m.

Answer 1

Using the conservation of energy formula, where kinetic energy is converted to potential energy, the maximum change in height for a 78.0 kg pole vaulter running at 8.21 m/s is approximately 3.50 meters.

Step-by-step explanation:

To find the maximum change in height that a 78.0 kg pole vaulter can rise when running at a speed of 8.21 m/s, we can apply the conservation of energy principle where the kinetic energy at the beginning is converted into potential energy at the maximum height. The formula for kinetic energy (KE) is ½mv² and for potential energy (PE) is mgh, where m is mass, v is velocity, g is the acceleration due to gravity (9.81 m/s²), and h is height. Setting KE equal to PE and solving for height (h) gives us:

h = ½v² / g

Substituting the given values:

h = (½ * (8.21 m/s)²) / (9.81 m/s²)

h = (0.5 * 67.3641 m²/s²) / 9.81 m/s²

h = 34.3641 m²/s² / 9.81 m/s²

h ≈ 3.50 m

Therefore, the maximum height change the pole vaulter can expect to achieve is approximately 3.50 meters.