What is the kinetic energy of a 1 kilogeram ball is thrown into the air with a velocity of 30m/sec?
How much potential energy does the ball have when it reaches the top of its ascent?
How high into the air did the nall travel?
Please help me help my child with her homework?
K.E. = (1/2)M V^2 = 450 Joules
You can find that equation in my previous answer.
The Potential Energy at the top of the throw will be the same (450 J), since the velocity will be zero there, and the sum of Potential and Kinetic Energy does not change.
For the height H that is reached, solve
M g H = 450 joules
H = 450/(M*g) = 450/(1*9.8) = 45.9 m
Step 1: Calculate the kinetic energy of the ball when it is thrown into the air.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the ball = 1 kilogram
Velocity of the ball = 30 meters per second
Substituting the values into the formula:
Kinetic Energy = (1/2) * 1 kg * (30 m/s)^2
Step 2: Calculate the potential energy of the ball when it reaches the top of its ascent.
The formula for potential energy is:
Potential Energy = mass * acceleration due to gravity * height
Given:
Mass of the ball = 1 kilogram
Acceleration due to gravity = 9.8 meters per second squared (approximate value)
Height = to be calculated
Step 3: Calculate the height of the ball's ascent.
We can use the equation of motion: vf^2 = vi^2 + 2 * a * d
Here, vf = 0, vi = 30 m/s (initial velocity), a = - 9.8 m/s^2 (acceleration due to gravity), d is the displacement/height.
Rearranging the equation: d = (vf^2 - vi^2) / (2 * a)
Since vf = 0, the equation simplifies to: d = (0 - (30 m/s)^2) / (2 * (-9.8 m/s^2))
Now we can solve for the height:
Step 1: Calculating the kinetic energy:
Kinetic Energy = (1/2) * 1 kg * (30 m/s)^2
= 450 joules
Step 2: Calculating the potential energy:
Potential Energy = 1 kg * 9.8 m/s^2 * height
= height * 9.8 joules
Step 3: Calculating the height of the ball's ascent:
height = (0 - (30 m/s)^2) / (2 * (-9.8 m/s^2))
= 45.92 meters
Therefore, the answers are:
- The kinetic energy of the ball is 450 joules.
- The potential energy of the ball when it reaches the top of its ascent is 45.92 * 9.8 joules.
- The ball traveled 45.92 meters into the air.
Sure, I'd be happy to help!
To calculate the kinetic energy of an object, you can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, the mass of the ball is given as 1 kilogram and the velocity is given as 30 meters per second. Plugging these values into the formula, we get:
Kinetic Energy = (1/2) * 1 kg * (30 m/s)^2
= (1/2) * 1 kg * 900 m^2/s^2
= 450 Joules
Therefore, the kinetic energy of the ball is 450 Joules.
Moving on to the potential energy, when the ball reaches the top of its ascent, all of its kinetic energy will be converted into potential energy due to the force of gravity. The formula to calculate potential energy is:
Potential Energy = mass * gravity * height
The mass of the ball is 1 kilogram, and the acceleration due to gravity on Earth is approximately 9.8 meters per second squared. The height is not given, so we'll need to calculate it.
At the top of its ascent, the ball's velocity will be zero. We can use the following equation to find the height:
Final Velocity^2 = Initial Velocity^2 + 2 * acceleration * distance
Since the final velocity is zero, we have:
0 = (30 m/s)^2 + 2 * (-9.8 m/s^2) * distance
Simplifying the equation, we get:
0 = 900 m^2/s^2 - 19.6 m/s^2 * distance
Solving for distance, we find:
Distance = 900 m^2/s^2 / (19.6 m/s^2)
= 45.9 meters
Now that we know the height is 45.9 meters, we can calculate the potential energy:
Potential Energy = 1 kg * 9.8 m/s^2 * 45.9 m
= 446.82 Joules
Therefore, the ball has a potential energy of approximately 446.82 Joules when it reaches the top of its ascent.
I hope this explanation helps you and your child with the homework! If you have any further questions, feel free to ask.