Question 16 (1 point) Retake question A 50.0 kg athlete jumps vertically upward from the ground to a height of 0 .90 m above the ground Determine the initial speed of the athlete. 9.4m/s 9.5m/s 4.2m/s 4.20m/s

Here's how to solve this problem using the conservation of energy principle:<br /><br />**1. Understand the Principle:**<br /><br />The athlete's total mechanical energy (the sum of kinetic and potential energy) remains constant throughout the jump, neglecting air resistance. At the start of the jump, all energy is kinetic. At the highest point, all energy is potential.<br /><br />**2. Define Variables:**<br /><br />* *m* = mass of the athlete (50.0 kg)<br />* *h* = maximum height reached (0.90 m)<br />* *g* = acceleration due to gravity (9.8 m/s²)<br />* *v* = initial velocity (what we want to find)<br /><br />**3. Set up the Equation:**<br /><br />Initial kinetic energy (KE) = Final potential energy (PE)<br /><br />(1/2) * m * v² = m * g * h<br /><br />**4. Solve for v:**<br /><br />Notice that the mass (m) cancels out on both sides:<br /><br />(1/2) * v² = g * h<br /><br />v² = 2 * g * h<br /><br />v = sqrt(2 * g * h)<br /><br />**5. Calculate:**<br /><br />v = sqrt(2 * 9.8 m/s² * 0.90 m)<br /><br />v = sqrt(17.64 m²/s²)<br /><br />v ≈ 4.2 m/s<br /><br />**Answer:**<br /><br />The initial speed of the athlete is approximately 4.2 m/s. The closest answer choice is 4.2m/s.<br />