Physics Calculation: Potential Energy at Maximum Height

This section details the calculation for the potential energy a body possesses at its maximum height when projected vertically upwards.

Step 1: Calculate Maximum Height Reached

First, we determine the maximum height ($h$) the body reaches. At the peak of its trajectory, the body's instantaneous velocity ($v$) becomes zero. We use the kinematic equation relating velocity, initial velocity ($u$), acceleration ($a$), and displacement ($s$):

$v^2 = u^2 + 2as$

Given values:

• Initial velocity, $u = 10 \text{ m/s}$
• Final velocity at maximum height, $v = 0 \text{ m/s}$
• Acceleration due to gravity, $a = -g = -10 \text{ m/s}^2$ (negative sign indicates upward motion is opposed by gravity)
• Displacement, $s = h$ (the maximum height)

Substitute these values into the equation:

$0^2 = (10 \text{ m/s})^2 + 2(-10 \text{ m/s}^2)h$

$0 = 100 \text{ m}^2/\text{s}^2 - (20 \text{ m/s}^2)h$

Rearrange to solve for $h$:

$(20 \text{ m/s}^2)h = 100 \text{ m}^2/\text{s}^2

$h = \frac{100 \text{ m}^2/\text{s}^2}{20 \text{ m/s}^2}$

$h = 5 \text{ m}$

The maximum height attained by the body is 5 meters.

Step 2: Calculate Potential Energy

The potential energy ($PE$) at the maximum height is calculated using the formula:

$PE = mgh$

Given values:

• Mass, $m = 10 \text{ kg}$
• Acceleration due to gravity, $g = 10 \text{ m/s}^2$
• Maximum height, $h = 5 \text{ m}$

Substitute these values:

$PE = (10 \text{ kg}) \times (10 \text{ m/s}^2) \times (5 \text{ m})$

$PE = 500 \text{ kg} \cdot \text{m}^2/\text{s}^2$

$PE = 500 \text{ J}$

Final Answer

The potential energy possessed by the body at its maximum height is 500 Joules.