Overview:

To calculate the kinetic energy (KE) and potential energy (PE) of a ball halfway up when thrown vertically upwards, we need to understand the concepts of kinetic and potential energy and apply the relevant formulas.

Explanation:

Kinetic Energy:
- Kinetic energy is the energy possessed by an object due to its motion.
- The formula to calculate kinetic energy is KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

Given data:
- Mass of the ball (m) = 0.1 kg
- Initial velocity (v) = 20 m/s

Let's calculate the kinetic energy of the ball using the given formula:

KE = 1/2 * m * v^2
= 1/2 * 0.1 kg * (20 m/s)^2
= 1/2 * 0.1 kg * 400 m^2/s^2
= 1/2 * 40 kg * m^2/s^2
= 20 kg * m^2/s^2

Therefore, the kinetic energy of the ball halfway up is 20 kg * m^2/s^2.

Potential Energy:
- Potential energy is the energy possessed by an object due to its position or height.
- The formula to calculate potential energy is PE = m * g * h, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

Given data:
- Mass of the ball (m) = 0.1 kg
- Acceleration due to gravity (g) = 9.8 m/s^2
- Height halfway up (h) = ?

To calculate the height halfway up, we need to consider the projectile motion of the ball. At the highest point, the velocity of the ball becomes zero.

Using the equation of motion:
v^2 = u^2 - 2 * g * h

Where:
v = final velocity (0 m/s at the highest point)
u = initial velocity (20 m/s)
g = acceleration due to gravity (9.8 m/s^2)
h = height halfway up

0^2 = (20 m/s)^2 - 2 * 9.8 m/s^2 * h
0 = 400 m^2/s^2 - 19.6 m/s^2 * h
19.6 m/s^2 * h = 400 m^2/s^2
h = 400 m^2/s^2 / 19.6 m/s^2
h ≈ 20.41 meters

Therefore, the height halfway up is approximately 20.41 meters.

Now, let's calculate the potential energy of the ball using the given formula:

PE = m * g * h
= 0.1 kg * 9.8 m/s^2 * 20.41 meters
= 0.1 kg * 200.218 m^2/s^2
= 20.0218 kg * m^2/s^2

Therefore, the potential energy of the ball halfway up is approximately 20.0218 kg *