A student drops the same 10 kilogram bowling ball three speedster times she drops the ball from heights of 1 meter 2 meters and 3 meters which graph correctly shows the balls kinetic energy when dropped from each height
Based on the information given, the correct graph would show the kinetic energy of the ball as a function of height dropped.
Let's analyze the situation:
- The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
- The velocity of an object when it hits the ground from a certain height can be determined using the equation v = sqrt(2 * g * h), where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height.
- We are assuming no other forces are acting on the ball except for gravity.
Now, based on these formulas and the information given, we can plot the kinetic energy of the ball as shown in the graph.
X-axis: Height of drop (in meters)
Y-axis: Kinetic energy (in Joules)
As the height increases, the kinetic energy of the ball will also increase because it will gain more speed as it falls from a greater height. Therefore, the correct graph should show a positive relationship between height and kinetic energy.
So, the correct graph would show a line that starts at 0 Joules when the height is 0 meters and increases as the height increases. Since the kinetic energy is directly proportional to the height, the graph would be a straight line passing through the origin with a positive slope.
Please note that I can't provide a visual graph as I am a text-based AI model, but you can use the information above to draw the correct graph on a piece of paper or in a graphing software.
To determine the kinetic energy of the bowling ball when dropped from different heights, we can use the formula:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Since the mass of the bowling ball is given as 10 kilograms, we can calculate the velocity of the ball when it hits the ground using the formula: velocity = sqrt(2 * acceleration * height)
Where acceleration due to gravity (g) is approximately 9.8 m/s^2.
Now, let's calculate the velocities and kinetic energies for each height:
1 meter height:
velocity = sqrt(2 * 9.8 * 1) = sqrt(19.6) ≈ 4.43 m/s
KE = 1/2 * 10 * (4.43)^2 ≈ 97.96 Joules
2 meters height:
velocity = sqrt(2 * 9.8 * 2) = sqrt(39.2) ≈ 6.26 m/s
KE = 1/2 * 10 * (6.26)^2 ≈ 195.74 Joules
3 meters height:
velocity = sqrt(2 * 9.8 * 3) = sqrt(58.8) ≈ 7.67 m/s
KE = 1/2 * 10 * (7.67)^2 ≈ 294.18 Joules
Now, let's draw a graph correctly representing the kinetic energy of the ball dropped from each height:
On the x-axis, we will have the height in meters, and on the y-axis, we will have the kinetic energy in Joules.
The graph should show three data points:
(1, 97.96)
(2, 195.74)
(3, 294.18)
Connecting these points will show how the kinetic energy changes with the height.
To determine the kinetic energy of the bowling ball when dropped from different heights, we can use the formula:
Kinetic energy (KE) = 1/2 * mass * velocity^2
Since the object falls freely in our case, the velocity can be calculated using the formula:
Velocity (v) = √(2 * acceleration * height)
Where acceleration due to gravity (g) is approximately 9.8 m/s^2.
Now let's calculate the velocity for each height:
Height = 1 meter:
v1 = √(2 * 9.8 m/s^2 * 1 m) = √19.6 m^2/s^2 ≈ 4.43 m/s
Height = 2 meters:
v2 = √(2 * 9.8 m/s^2 * 2 m) = √39.2 m^2/s^2 ≈ 6.26 m/s
Height = 3 meters:
v3 = √(2 * 9.8 m/s^2 * 3 m) = √58.8 m^2/s^2 ≈ 7.67 m/s
Now we can calculate the kinetic energy for each height using the formula mentioned earlier:
KE = 1/2 * mass * velocity^2
Given that the mass (m) is 10 kg, we can calculate the kinetic energy for each height:
KE1 = 1/2 * 10 kg * (4.43 m/s)^2
KE2 = 1/2 * 10 kg * (6.26 m/s)^2
KE3 = 1/2 * 10 kg * (7.67 m/s)^2
Now we can plot a graph to show the kinetic energy of the ball from each height.
The x-axis represents the heights (1m, 2m, 3m), and the y-axis represents the corresponding kinetic energy values.
The graph should show an increasing trend since kinetic energy is proportional to the square of the velocity.
Please note that the values provided here are approximate calculations, and some rounding may have occurred.