a 1kg ball is thrown into the air with an initial velocity of 30 m/sec. how much kinetic energy does the ball have?
-how much potential energy does the ball have when it reaches the top of its ascent?
-how high into the air did the ball travel?
Assume potential energy on ground is zero.
Kinetic energy at 30 m/s
=(1/2)mv²
Potential energy at highest point, H from ground
=mgh
Equate energies,
mgh=(1/2)mv²
h=(1/2)mv²/mg
=v²/(2g)
To calculate the kinetic energy of the ball, we can use the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the ball is 1 kg and the initial velocity is 30 m/s, let's substitute the values into the equation:
Kinetic Energy = (1/2) * 1 kg * (30 m/s)^2
Simplifying the equation:
Kinetic Energy = 0.5 * 1 kg * 900 m^2/s^2
Kinetic Energy = 450 J
Therefore, the ball has 450 Joules of kinetic energy.
To calculate the potential energy of the ball at the top of its ascent, we can use the equation:
Potential Energy = mass * gravity * height
Given that the mass of the ball is 1 kg and acceleration due to gravity is approximately 9.8 m/s^2, let's substitute the values into the equation:
Potential Energy = 1 kg * 9.8 m/s^2 * height
Since the ball has reached the top of its ascent, its velocity at this point is 0 m/s. Therefore, all its initial kinetic energy has been converted into potential energy.
450 J (kinetic energy) = 1 kg * 9.8 m/s^2 * height
Simplifying the equation:
450 J = 9.8 m/s^2 * height
height = 450 J / (9.8 m/s^2)
height ≈ 45.9 m
Therefore, the ball reaches a height of approximately 45.9 meters.
To summarize:
- The ball has 450 Joules of kinetic energy.
- The ball has approximately 45.9 meters of potential energy at the top of its ascent.
To calculate the kinetic energy of the ball, we can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the ball is 1kg and the initial velocity is 30 m/sec, we can substitute these values into the formula:
Kinetic Energy = (1/2) * 1kg * (30 m/sec)^2
Kinetic Energy = 0.5 * 1kg * 900 m^2/sec^2
Kinetic Energy = 450 Joules
Therefore, the ball has 450 Joules of kinetic energy.
Now, let's calculate the potential energy of the ball when it reaches the top of its ascent. At the highest point, the ball has no kinetic energy, but it has potential energy due to its height above the ground.
The potential energy can be calculated using the formula:
Potential Energy = mass * gravity * height
The mass of the ball is 1kg, and the acceleration due to gravity can be assumed as approximately 9.8 m/s^2. To find the height, we need to know the acceleration and time spent during ascent, which is not provided in the question. Without this information, we cannot determine the exact potential energy at the top of the ascent.
To find the maximum height the ball traveled, we can use the following formula for vertical motion:
Final Velocity^2 = Initial Velocity^2 + 2 * acceleration * distance
In this case, since we're interested in the height, the final velocity is 0 m/s (at the top of the ascent). The initial velocity is 30 m/s, and the acceleration due to gravity is -9.8 m/s^2 (negative because it's acting against the initial velocity).
Solving for distance (height):
0^2 = (30 m/s)^2 + 2 * (-9.8 m/s^2) * distance
Simplifying the equation:
0 = 900 m^2/s^2 + (-19.6 m/s^2) * distance
19.6 m/s^2 * distance = 900 m^2/s^2
distance = 900 m^2/s^2 / 19.6 m/s^2
distance ≈ 45.9 meters
Therefore, the ball traveled approximately 45.9 meters into the air.