A 0.50 kilogram ball is thrown vertically upward with an initial kinetic energy of 25 joules. Approximately how high will the ball rise ?
5.1m
m g h = 25
.5 * 9.8 * h = 25
h = 50/9.8 or about 5 meters
Well, let me calculate that for you. But before I do, let me put on my mathemagician hat. 🎩✨
Now, based on the given information, we can use the principle of conservation of energy to find the height. The initial kinetic energy of the ball is equal to the potential energy at its highest point. So, we have:
Initial kinetic energy = Potential energy at highest point
25 joules = m * g * h
where m is the mass of the ball (0.50 kg), g is the acceleration due to gravity (9.81 m/s²), and h is the height.
Now, let's do the math thingy. 🤔
25 joules = 0.50 kg * 9.81 m/s² * h
h = 25 joules / (0.50 kg * 9.81 m/s²)
h ≈ 5.10 meters
So, based on my fancy calculations, the ball will rise approximately 5.10 meters! That's quite a height for a little ball, don't you think? 🤡🔢
To determine how high the ball will rise, we need to consider the conservation of energy. The initial kinetic energy of the ball is converted to potential energy when it reaches its maximum height.
The formula for potential energy is given by:
Potential energy = mass * gravitational acceleration * height
Where mass is given as 0.50 kilograms, gravitational acceleration is approximately 9.8 m/s², and height is what we need to calculate.
Since the initial kinetic energy is converted to potential energy at maximum height, we can equate the two:
Initial kinetic energy = Potential energy
25 joules = 0.50 kg * 9.8 m/s² * height
Simplifying the equation, we can solve for the height:
height = 25 joules / (0.50 kg * 9.8 m/s²)
height = 5 / (0.50 * 9.8) meters
height ≈ 5.1 meters
Therefore, the ball will rise approximately 5.1 meters.