We can solve the problem by using the concept of conservation of energy or the kinematic equation for vertical motion.

Since air resistance is neglected, all the initial kinetic energy is converted into gravitational potential energy at the highest point of the jump.

Step 1: Use Energy Conservation

The formula for kinetic energy is: $KE = \frac{1}{2} m v^2$ Where:

• $m = 60 \, \text{kg}$ (mass of the person),
• $v = 3 \, \text{m/s}$ (initial speed when leaving the ground).

The gravitational potential energy (PE) at the maximum height $h$ is: $PE = mgh$ Where:

• $g = 9.8 \, \text{m/s}^2$ (gravitational acceleration),
• $h$ is the height we want to calculate.

At the maximum height, the kinetic energy is fully converted to potential energy, so: $\frac{1}{2} m v^2 = mgh$

Step 2: Simplify and Solve for $h$

Cancel out the mass $m$ from both sides: $\frac{1}{2} v^2 = gh$ Now, solve for $h$: $h = \frac{v^2}{2g}$

Step 3: Substitute the values

$h = \frac{(3)^2}{2 \times 9.8} = \frac{9}{19.6}$ $h = 0.46 \, \text{m}$

Answer:

The maximum height the person can reach is 0.46 meters (rounded to 2 significant figures).

Would you like further details or have any other questions? Here are 5 related questions for practice:

1. How would air resistance affect the height the person can reach?
2. What if the person left the ground with a speed of 4 m/s? How would that change the result?
3. How does the gravitational field strength affect the maximum height?
4. What is the maximum height a person can reach on the Moon, where $g = 1.62 \, \text{m/s}^2$?
5. How much kinetic energy does the person have initially?

Tip: When solving physics problems involving energy, always consider whether external forces like friction or air resistance need to be taken into account.